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What is the value of lambda for which t...

What is the value of `lambda ` for which the vectors `3hat(i)+4hat(j)-hat(k) and -2hat(i)+lambda hat(j)+10hat(k)` are perpendicular?

A

1

B

2

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
D
Given vectors are `3hat(i)+4hat(j)-hat(k) and -2hat(i)+lambdahat(j)+10hat(k)`.
If these are perpendicular, dot product is 0.
`(3hat(i)+4hat(j)-hat(k)).(-2hat(i)+lambdahat(j)+10hat(k))=0`
`rArr (3)(-2)+(4)(lambda)+(-10)=0`
`rArr - 6 +4lambda-10=0`
`rArr 4lambda=16`
`rArr lambda=4`
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