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Let a= hat(i) - hat(j) , b=hat(i) + hat(...

Let `a= hat(i) - hat(j) , b=hat(i) + hat(j) + hat(k)` and c be a vector such that `axx c + b=0 " and " a. c =4, ` then `|c|^(2)` is equal to

A

8

B

`(19)/(2)`

C

9

D

`(17)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have `(vec(a) xx vec(c )) + b=0`
`rArr a xx (vec(a) xx vec(c )) + axx b=0`
(taking cross product with a on both sides )
`rArr (vec(a) ". " vec(c )) a- (a .a ) c + |{:(hat(i),,hat(j),,hat(k)),(1,,-1,,0),(1,,1,,1):}|=0`
`[ :' a xx (b xx c ) = (a . c) b -(a. b) c]`
`rArr 4(hat(i) - hat(j)) - 2c + (-hat(i) -hat(j) + 2hat(k)) =0`
`[ :' a . a = (hat(i) - hat(j)) =1+1 =2 " and " a.c =4]`
`rArr 2c =4 hat(i) -4hat(j) -hat(i) -hat(j) +2hat(k)`
`rArr c = (3hat(i) -5hat(j) +2hat(k))/(2) rArr |c|^(2) = (9+25+4)/(4) =(19)/(2)`
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