Answer to Question #58423 in Vector Calculus for Joseph

Question

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