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If the volume of a parallelepied having ...

If the volume of a parallelepied having `vec(a)=(5hat(i)-4hat(j)+hat(k)), vec(b)=(4hat(i)+3hat(j)+lambdahat(k)) and vec(c)=(hat(i)-2hat(j)+7hat(k))` as coterminous edges, is 216 cubic units then the value of `lambda` is

A

`(5)/(3)`

B

`(4)/(3)`

C

`(2)/(3)`

D

`(1)/(3)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(vec(a)xxvec(b)).vec(c)=|(5,-4,1),(4,3,lambda),(1,-2,7)|=5(21+2lambda)+4(28-lambda)+1.(-8-3)`
`=(105+112-11)+(10lambda-4lambda)=(206+6lambda)`.
`:. 206 + 6 lambda=216 rArr 6 lambda=10 rArr lambda=(10)/(6)=(5)/(3)`.
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