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If the planes vecr.(hati+hatj+hatk)=q(1)...

If the planes `vecr.(hati+hatj+hatk)=q_(1),vecr.(hati+2ahatj+hatk)=q_(2)andvecr.(ahati+a^(2)hatj+hatk)=q_(3)` intersect in a line, then the value of `a` is

A

1

B

`1//2`

C

2

D

0

Text Solution

Verified by Experts

The correct Answer is:
a, b
`vecr*vec(n_1)=vec(q_1) and vecr*vec(n_2)=vecq_(2), vecr*vecn_(3)= vecq_(3) `
intersect in a line if `[vecn_(1) vecn_(2) vecn_(3)]=0`. So,
`" "|{:(1,,1,,1),(1,,2a,,1),(a,,a^(2),,1):}|=0`
or `" "2a-a^(2)-1+a+a^(2)-2a^(2)=0`
or `" "2a^(2)-3a+1=0`
or `" "a=1//2, 1`
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