MTH282
Two vectors are said to be equal if their --------- are equal.
magnitudes and directions
Two vectors A, B, are said to collinear ( linearly dependent) if there are scalar a and b such aA + bB = 0 implies -----
a and b are not all zero
Collinear vectors are said be --------
linearly dependent
Find the unit vector in the direction of the vector 3i + 2j + 6k.
(3i + 2j + 6k)/7
The following are true about scalar product of vectors accept -----
j. j = 1
Given that v = 2i + j + 5k and u = 3i -4j + k, find v.u
7
Find the direction cosines of the vector 3i + 4j
3/5, 4/5
Find sum of direction cosines of the vector 3i + 2j + 6k.
1/7
Given that vector D= 2i - 3j + 5k and P = 4i + j + 6k find D.P
35
If vector OC = 2i + j and vector OB= 6i -2j, find the magnitude of vector CB
5
Find the vector product of A = i + j+K and B = 3i +3j+3K
0
Find the acute angle (to the nearest degree) angle between the vectors a=-3i+4j and
b=5i+12j.
59.49°
Find a vector that is of magnitude 6 units and is collinear to the vector i+j.
32i+32j
Given that A =2i + j-3k, B = i- 2j+k C= i +j -4k. Evaluate A. (BC).
10
Find the unit vector perpendicular to the plane of the vectors A=3i-2j+4k and
B= i+j-2k
15(2i+j)
An object moves in a straight curve R t32t) i -3e2t j +2sin 5tk, Find its velocity at time t=1.
5i +0.812 j+ 2.837k
If the scalar product of vectors 2i - j -4k and 5i - 2j –mk is four, find m.
-2
Find the angle between the vectors 2i-4 j +k and 2i -3j -3k.
cos-1(0.6048)
Determine s such that the vectors s i +4 j +4k and –2 i + 5j +sk perpendicular.
-10
Find the value of a that makes the vectors 5 i -a j +2k and i + 3j +5k perpendicular.
5
Determine n such that the vectors 5i +n j -5k and -4 i + nj +k are perpendicular.
5
Determine the unit vector parallel to the sum of vectors 3i +4 j -5k and i + 8j +9
12i+4j+3k13
Find the scalar product of the vector -2i-j-2k and the unit vector parallel to the vector 4i+3j-12k
1
Find the vector product of v = (1, 0,2) and u = (2, 4, 3).
(-8,1, 4)
Find the gradient of the scalar field ∅ x, y, z=x3yz2 at the point (1,1,1)
3i + j +2k
If that ∅=x4y+z2, find the Laplacian of ∅
2(6x2 +1)
Given that R=xzi-y2j+2x2yk , find ∇.(∇xR)
0
Given that R=xzi-y2j+2x2yk , find the divergence of R
z-2y
Given that ∅=3y2x+x2z2, find ∇∅
(3y2+2xz2)i+6yxj+2zx2k
If ∅=3y2x+x2z2 , find ∇2∅.
2z2+6x+2x2
Given that =yxi+yx2j+2zyk , find (∇xA)
2zi+x(2y-1)k
Given that T=y2x2i+x2z2 j+y2z2k. find curl of T.
2z (yz-x2)i+2x(z2-yx)k
Given that T=y2x2i+x2z2 j+y2z2k. find curl of T at point (1, -1,1)
-4i+4k
The scalar product of vectors a and b, where θ is the angle between them, is .........
|a||b| cos θ
If that ∅=x2z-yz2, find the Laplacian of ∅
2z-2y
If that ∅=x2y2z2, find the Laplacian of ∅.
2(y2z2+x2z2+x2y2)
Given thatA =yxi+yx2j+2zyk , find ∇x(∇xA)
2xi-(2y-3)j
Let =yxi+xzj+zyk , find ∇x(∇xE) .
-2j
Find the Jacobian of the transformation x=Rsinθcos∅, y=Rsinθ sin∅ and z=Rcos∅ with respect to R , θ and ∅
-R2sinθ
Determine the Jacobian of x=u+v, y=2v with respect to u and v
2
Given that u =x+2y and v=x - y, find the Jacobian of the transformation x and y with respect to u, and v
-1/3
Find the Jacobian of x=u+v +s, y=2v-s and z=u-v with respect to u, v and s
-5
Given that x=2s – w, y=v+s+2w and z = 2v-s -w find the Jacobian of the transformation x and y with respect to v , s and w5
13
Let ∂x, y∂u, v be the Jacobian of the transformation x and y with respect to u and v, then ∂x, y∂u, v is equal to --------
-∂y, x∂u, v
Expand 1-i1+i4
1
Let F(z)= 7-z1-z2 and z =1+2i. Find F(z).
1+i/2
Given that R =y2zx2i+xj-y4zx3k , find ∇.R .
2xy2zi+y4x3k
Given that u =x+4y and v=x-3y, find the Jacobian of the transformation x and y with respectt to u , and v
-2
Given that u =x+2y and v=x - y, find the Jacobian of the transformation x and y with respect to u and v
-1/7
Given that =zxi+zyj+yxk , find ∇x(∇xA)
2k
Two vectors are said to be equal if their --------- are equal.
magnitudes and directions
Two vectors A, B, are said to collinear ( linearly dependent) if there are scalar a and b such aA + bB = 0 implies -----
a and b are not all zero
Collinear vectors are said be --------
linearly dependent
Find the unit vector in the direction of the vector 3i + 2j + 6k.
(3i + 2j + 6k)/7
The following are true about scalar product of vectors accept -----
j. j = 1
Given that v = 2i + j + 5k and u = 3i -4j + k, find v.u
7
Find the direction cosines of the vector 3i + 4j
3/5, 4/5
Find sum of direction cosines of the vector 3i + 2j + 6k.
1/7
Given that vector D= 2i - 3j + 5k and P = 4i + j + 6k find D.P
35
If vector OC = 2i + j and vector OB= 6i -2j, find the magnitude of vector CB
5
Find the vector product of A = i + j+K and B = 3i +3j+3K
0
Find the acute angle (to the nearest degree) angle between the vectors a=-3i+4j and b=5i+12j.
59.49°
Find a vector that is of magnitude 6 units and is collinear to the vector i+j.
32i+32j
Given that A =2i + j-3k, B = i- 2j+k, C= i +j -4k. Evaluate A. (BxC).
10
Find the unit vector perpendicular to the plane of the vectors A=3i-2j+4k and
B= i+j-2k
15(2i+j)
5i +0.812 j+ 2.837k
If the scalar product of vectors 2i - j -4k and 5i - 2j –mk is four, find m.
-2
Find the angle between the vectors 2i-4 j +k and 2i -3j -3k.
cos-1(0.6048)
Determine s such that the vectors s i +4 j +4k and –2 i + 5j +sk perpendicular.
-10
Find the value of a that makes the vectors 5 i -a j +2k and i + 3j +5k perpendicular.
5
Determine n such that the vectors 5i +n j -5k and -4 i + nj +k are perpendicular.
5
Determine the unit vector parallel to the sum of vectors 3i +4 j -5k and i + 8j +9
12i+4j+3k13
Find the scalar product of the vector -2i-j-2k and the unit vector parallel to the vector 4i+3j-12k
1
Find the vector product of v = (1, 0,2) and u = (2, 4, 3).
(-8,1, 4)
Find the gradient of the scalar field ∅ x, y, z=x3yz2 at the point (1,1,1)
3i + j +2k
If that ∅=x4y+z2, find the Laplacian of ∅
2(6x2 +1)
Given that R=xzi-y2j+2x2yk , find ∇.(∇xR)
0
Given that R=xzi-y2j+2x2yk , find the divergence of R
z-2y
Given that ∅=3y2x+x2z2, find ∇∅
(3y2+2xz2)i+6yxj+2zx2k
If ∅=3y2x+x2z2 , find ∇2∅.
2z2+6x+2x2
Given that =yxi+yx2j+2zyk , find (∇xA)
2zi+x(2y-1)k
Given that T=y2x2i+x2z2 j+y2z2k. find curl of T.
2z (yz-x2)i+2x(z2-yx)k
Given that T=y2x2i+x2z2 j+y2z2k. find curl of T at point (1, -1,1)
-4i+4k
The scalar product of vectors a and b, where θ is the angle between them, is .........
|a||b| cos θ
If that ∅=x2z-yz2, find the Laplacian of ∅
2z-2y
If that ∅=x2y2z2, find the Laplacian of ∅.
2(y2z2+x2z2+x2y2)
Given that A =yxi+yx2j+2zyk , find ∇x(∇xA)
2xi-(2y-3)j
Let E=yxi+xzj+zyk , find ∇x(∇xE) .
-2j
Find the Jacobian of the transformation x=Rsinθcos∅, y=Rsinθ sin∅ and z=Rcos∅ with respect to R , θ and ∅
-R2sinθ
Determine the Jacobian of x=u+v, y=2v with respect to u and v
2
Given that u =x+2y and v=x - y, find the Jacobian of the transformation x and y with respect to u, and v
-1/3
Find the Jacobian of x=u+v +s, y=2v-s and z=u-v with respect to u, v and s
-5
Given that x=2s – w, y=v+s+2w and z = 2v-s -w find the Jacobian of the transformation x and y with respect to v , s and w5
13
Let ∂x, y∂u, v be the Jacobian of the transformation x and y with respect to u and v, then ∂x, y∂u, v is equal to --------
-∂y, x∂u, v
Expand 1-i1+i4
1
Let F(z)= 7-z1-z2 and z =1+2i. Find F(z).
1+i/2
Given that R =y2zx2i+xj-y4zx3k , find ∇.R .
2xy2zi+y4x3k
Given that u =x+4y and v=x-3y, find the Jacobian of the transformation x and y with respect to u , and v
-2
Given that u =x+2y and v=x - y, find the Jacobian of the transformation x and y with respect to u and v
-1/7
Given thatA =zxi+zyj+yxk , find ∇x(∇xA)
2k
A vector V with a unit vector a and magnitude k is written as V = -----
*Ka*
The unit vector in the direction of the resultant of vectors 2i -j + k and
i + j + 2k is......
*i + k*
If the scalar product of vectors i - j -k and 3i -2j –ak is eight, find a.
*3*
If A.B =0 then the angle between vectors is --------
*90*
If AxB =0 and A and B are not null vectors, then A and B are -------
*Parallel*
Find the acute angle between the vectors a=-4i-3j and b=5i-12 to nearest degree.
*58*
The vector product of a=2i+j+k and b=i+3j-2k is -----
*(17)-i+5j+5k*
Determine the acute angle between the vectors 2i+4j and 5i-4j to the nearest degree.
*78°*
Let ∅ (x, y, z) = constant c be an equation of a surface then, ∇∅ is ------to this surface.
*Normal*
If ∅ x, y, z=x4y6z4+xy . determine ∇x(∇∅)
*Zero*
Let ∅ x, y, z=x3y2z4 . determine curl of ∇∅
*0*
Find the gradient of the scalar field ∅ x, y, z=x3y2z4 at the point (1,1,1)
*3i+2j+4k*
Let ∂x, y∂u, v be the Jacobian of the transformation x and y with respect to u and v. Then ∂x, y∂u, u is equal to --------
*0*
Let ∂x, y∂u, v be the Jacobian of the transformation x and y with respect to u and v. Then ∂x, k∂u, v (where k is constant) is equal to --------
*0*
Determine the vector product of the vectors u=3i-j+k and v=4i+2j-k.
*-i+7j+10k*
Determine the scalar product of the vectors A =4i +2 j- 6k and B = i+ 6j+k
*10*
Given that A =2i + j-3k, B = i- j+2k, C= i +3j -k. Evaluate A. (BxC )
*-19*
Find the vector perpendicular to the plane of the vectors A= i-j+k and B= i+j-2k
*-i+3j+2k*
Given that A =2i + j-3k, B = i- j+2k C= i +3j -k. Evaluate C. (AxB)
*-19*
An object moves in a straight curve G=(t3+2t2+2t)i+3e(t-1)j+2tk. Find its acceleration at time t=1.
*10i +3j*
Find the unit vector in the direction of the sum of the vectors i +6j and 2i - 2j .
*3i/5+4i/5*
An object moves in a straight curve R=(3t2+t)i+3e(t-2)j+2k Find its velocity at time t=2.
*13i +3j*
Find the gradient of the scalar field ∅ x, y, z=4xzy2 at the point (1, 1, 2)
*8i +16j +4k*
Given that E=xzi-y2j+2x2yk , find ∇.E
*4xy*
Given that R=x+zi-y2j+2x2yk , find ∇.∇xR
*0*
Given that T=y2i+z2 j+x2k. find curl of T.
*2zi+2xj-2ky*
Given that P=y2i+z2 j+x2k.. find curl of P at point (2, 2, 2)
*4i+4j+4k*
Let the scalar product of vectors xi +3 j -5k and xi + j -2k be thirty eight. Find x.
*5*
The scalar product of vectors 2i + cj +6k and 3i + 5j -6k.is five, find c.
*7*
If that ∅=x2y2z2, find the Laplacian of ∅ at (1, -1, -1).
*6*
Given that A =yxi+yx2j+2zyk , find curl curl A at (3, -1, 5)
*6i+5j*
Let E=yxi+xzj+zyk , find magnitude of curl E
*2*
Find the Jacobian of the transformation x=(r+2)sinθ , y=(r+2)cosθ with respect to r and θ
* -(r+2)*
Determine the Jacobian of x=vcosθ , y=vsinθ with respect to v and θ
*V*
Determine the Jacobian of x=3u+2v, y=v with respect to u and v
*3*
Find the Jacobian of x=u-v +s, y=2u+v-s and z=v+s with respect to u, v and s
*6*
If A¯ is the conjugate of the complex number A, determine A¯ +A
2Re(z)*
Evaluate 1-i1+in where n is a positive even positive integer.
*1*
Evaluate 1-i1+in where n is a positive odd positive integer.
*-i*
Given that F(z)= 2-z1-z and z =1+i, find F(z)
*-1+2i*
Given that F(z)= 4+z1-z and z =1-i, find F(z)
*-1+5i*
Expand (1+2i)(1+i)(1-i).
*2+4i*
Find the real part of the complex number 4+i4-i2
*15/17*
If z=2(cosπ6+isinπ6), find z6
*-64*
Evaluate 1+i1-i8
*1*
Evaluate 1-i1+in where n is a positive odd positive integer.
*-i*
Given that u =3x+y and v=x -2y, find the Jacobian of the transformation x and y with respect to u, and v
*1*
Evaluate 1-i1+in where n is a positive even positive integer.
*1*
Given that u =x+y and v=2x-y, find the Jacobian of the transformation x and y with respectt to u , and v
*-1/3*
Evaluate 1-i1+in where n is a positive even positive integer.
*1*