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If vector vec a = hati + hatj + ...

If vector ` vec a = hati + hatj + hatk , vecb = 4 hati + 3 hatj + 4 hatk ` and ` vec c = hati + alpha hatj + beta hatk ` are linearly dependent and ` | vec c | = sqrt3 ` , then value of ` | alpha | + | beta | ` is

A

2

B

3

C

1

D

4

Text Solution

Verified by Experts

The correct Answer is:
A
`veca,vecb,vecc` are linearly dependent `rArr` Coplanar vectors
`|(1,1,1),(4,3,4),(1,alpha,beta)|=0`
`rArr 1+0-beta=0 rArr beta=1`
`rArr alpha^2=1 rArr alpha =pm 1 rArr |alpha|+|beta|=2`
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