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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
`vec(a) , vec(b) , vec(c)` are linerly depend `rArr` Coplanar vectors
`|{:(,1,1,1),(,4,3,4),(,1,alpha,beta):}|=0`
`rArr 1 + 0 - beta =0 rArr beta = 1`
`because |vec C| = sqrt(3) rArr 1 + alpha^(2) + beta alpha = pm 1 rArr |alpha | +| beta| = 2`
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