FIND A VECTOR WHOSE LENGTH IS 7 AND WHICH IS PERPENDICULAR TO EACH OF THE VECTORS A=2I+3J+6K AND B=I CAP+J CAP-K CAP
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Answer:
Given
A
=2
i
^
−3
j
^
+6
k
^
B
=
i
^
+
j
^
−
k
^
A
×
B
=−3
i
^
+8
j
^
+5
k
^
∣
A
×
B
∣=
(−3)
2
+(8)
2
+(5)
2
=
98
=7
2
Therefore required vectors
∣
A
×
B
∣
A
×
B
×7
=
7
2
−3
i
^
+8
j
^
+5
k
^
×7
=
2
−3
i
^
+8
j
^
+5
k
^
If multiply this vector by −1 it would have same magnitude at some time and perpendicular to A and B. Hence
2
3
i
^
−8
j
^
−5
k
^
is correct.
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