1.

The vectors a=2hati+hatj-2hatk, b=hati+hatj. If c is a vector such that a.c=|c| and |c-a|=2sqrt2, angle between axxb and c is 45^(@), then |(axxb)xxc| is

Answer»

3
`(sqrt3)/(2)`
`(3sqrt2)/(2)`
None of these

Solution :Now,`|a|^(2)=9 and |b|^(2) = 2 `
`therefore |C-a|^(2) =|c|^(2) +|a|^(2) -2C*a=8`
`=|c|^(2)+9-2|c| =8 RARR |c| = 1`
Now , ` a xx b = | (hati , hatj , hatk ) , ( 2, 1 , -2), (1, 1 , 0)|=2 hati - 2 hatj+ hatk `
` rArr | a xx b| = sqrt( 2^(2) +(-2)^(2)+1^(2))=3`
`therefore|(a xx b) xx c|=|a xx b||c|sin 45^(@) = 3(1) ((1)/(sqrt(2)))=(3sqrt(2))/(2)`


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