54 635
Assignments Done
98,2%
Successfully Done
In November 2017
Your physics homework can be a real challenge, and the due date can be really close — feel free to use our assistance and get the desired result.
Be sure that math assignments completed by our experts will be error-free and done according to your instructions specified in the submitted order form.
Our experts will gladly share their knowledge and help you with programming homework. Keep up with the world’s newest programming trends.

Vector Calculus Answers

164Questions:

141Free Answers by our Experts:

Ask Your question

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Search & Filtering

) For a scalar field ( , , ) ,
n n n
φ x y z = x + y + z show that (∇φ) r = nφ
r r
. , where n is a non-zero
real constant.
5. Given that vectors
a→=5i^−2j^+3k^
b→=3i^+j^−2k^
c→=i^−3j^+4k^
, calculate the scalar triple product
a⃗ ⋅(b⃗ ×c⃗ )

6. Given that vectors
a→=5i^−2j^+3k^,
b→=3i^+j^−2k^
and
c→=i^−3j^+4k^
, calculate the vector triple product
a⃗ ×(b⃗ ×c⃗ )
why there is no any particular rule to subtract vectors?
1 If
ϕ=2xz4−x2y
, find
|▽ϕ|
(√93)
(√80)
(√12)
(√110)

2 If
ϕ(x,y,z)=3x2y−y3z2
, find
▽ϕ
at point (1,-2,-1)
−12i−9j−16k
i−3j−k
2i−5j−6k
−3i−4j−2k

3 Find a unit normal to the surface
x2y+2xz=4
at point (2,-2,3)
23i−23j−23k
−15i+25j+25k
−13i+23j+23k
−17i+27j+27k

4 Let
ϕ(x,y,z)=xy2z
and
A=xzi−xy2j+yz2k
,find
∂3∂x2∂z(ϕA)
2i+2j−5k
5i−k
4i−2j
i+j

5 Given that
ϕ=2x2y−xz3
find
▽2ϕ
2y−6xz
4y−6xz
2y−xz
y+6xz

6 If
A=xz3i−2x2yzj+2yz4
, find
▽×A
at point (1,-1,1).
2j+3k
2i+j74k
i+3j+5k
3j+4k

7 Given that
A=A1i+A2j+A3k
and
r=xi+yj+zk
, evaluate
▽⋅(A×r)
if
▽×A=0
0
3
2
5

8 Let
A=x2yi−2xzj+2yzk
, find Curl curl A.
3j+4k
2x+2)k
(2x+2)j
3j−4k

9 Given
A=2x2i−3yzj+xz2k
and
ϕ=2z−x3y
, find
A⋅▽ϕ
at point (1,-1,1).
5
3
4
1

10 Find the directional derivative of
ϕ=x2yz+4xz2
at (1,-2,-1) in the direction
2i−j−2k
373
353
253
113
1 Find the angle between
A=2x+2j−k
and
B=6i−3j+2k
600
450
690
790

2 Determine the value of a so that
A=2i+aj+k
and
B=4i−2j−2k
are perpendicular
a=5
a=3
a=1
a=7

3 Determine a unit vector perpendicular to the plane of
A=2i−6j−3k
and
B=4i+3j−k
±(37i−27j+67k)
±(35i+25j−65k)
±(14i−34j−12k)
±(−23i−13j+34k)

4 Find the work done in moving an object along a vector
r=3i+2j−5k
3
5
7
9

5 Given that
A=2i−j+3k
and
B=3i+2j−k
, find
A⋅B
3
6
1
9

6 If
A=2i−3j−k
and
B=i+4j−2k
, find
(A+B+×(A−B)
3i+4j+25k
2i+6j+2k
−20i−6j−22k
−3i−5j−25k

7 If
A=3i−j+2k
,
B=2i+j−k
and
C=i−2j+2k
, find
(A×B)×C
15i+15j−5k
5i+5j−5k
−10i+10j−5k
15i+10j−5k

8 Determine a unit vector perpendicular to the plane of
A=2i−6j−3k
and
B=4i+3j−k
35i−25j+65
17i−37j+47
37i−27j+67
27i−47j+57

9 Evaluate
(2i−3j)⋅[(i+j−k)×(3i−k)]
4
5
6
8

10 If
A=i−2j−3k
,
B=2i+j−k
and
C=i+3j−2k
,evaluate
(A×B)⋅C
-25
11
15
-20
Determine whether the vectors u and v are parallel, orthogonal, or neither.

u = <6, -2>, v = <8, 24>

a. Neither
b. Parallel
c. Orthogonal
If
A=x^z^3i−2^x^2yzj+2y^z^4
, find
▽×A
at point (1,-1,1).

2j+3k
\
2i+j74k

i+3j+5k

3j+4k
Let
A=2x^2i−3yzj+xz^2k
and
ϕ=2z−x^3y
, find
A.▽ϕ
at point (1,-1,1).
5
3
4
1
Let
A=x^2yi−2xzj+2yzk
, find Curl curl A.

3j+4k

2x+2)k

(2x+2)j

3j−4k
Let
ϕ=2x^z^4−x^2y
,find
|▽ϕ|

5(√97)

3(√112)

(√105)

2(√93)