1. 1
For what values of a are the
vectors 2 - 2
and 2 2
perpendicular?
a a
a a
A i j k
B i j k
Solution
2
2 - 2 ( 2 2
2 2 ( 1)
Put . 0 2 ( 1) 0
0
OR
1
,
. ( a a a a
= 2 - 4 2 =
w
2
No
i j k). i j k)
a.a a + a a a a a
A B a a
a
a
A B
2. 2
2 - ,
-2 3
- -
on
-
For the two vectors
i j k
i j k
Find
a and I l
b component of
c angle between and
d X
e X
A
B
A B A B
B A
A B
A B
A B A B
Solution
6. 6
1 0
.
cos
2 6 1
1 4 1 4 9 1
3 3
0.33
9.16
6 14
cos 0.33 71
A B
A B
(d)
7. 7
1 1
1 2 1 3
2 1
1 2 1 ( 1)
3 1
2 3 1
1 1 1 2
( 1) ( 1)
2 1 2 3
5 7
i j k
X i
j k
i j k
A B
(e)
8. 8
1 1
1 2 1 3
2 - ,
-2 3
- ( 2 - )
( 2 3
1 2
( 1)
5 0
3 2 3 1
( 1)
)
3 2
( 2 - )
( 2 3 )
5
( 1)
1 0 1 5
10 2 14
( - ) ( ) 3 1 2
1 5 0
i j k
i j k
i j k
i j k
i j k
i
i
j k
i j
j k
i j k
i j
i j k
X
k
A
B
A B
A B
A B A B
