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Let vec a = hati + lamda1 hatj + hatk , ...

Let `vec a = hati + lamda_1 hatj + hatk , vec b = 2 hati + ( 1 - lamda_2) hatj + 2 hatk " and" vec c = hati + hatj + (lamda_3 - 2) hatk` be the vectors such that `vecb = 2veca` and ` veca` is perpendicular to `vec c` . Then a possible value of ` (lamda_1 , lamda_2 , lamda_3)` is :

A

`(1/3, 4/3, 2/3)`

B

`(1/2 , 0 , - 1)`

C

`(4, - 3, 1)`

D

`(1/3 , 1/3 , 2/3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`veca = hati + lamda_1 hatj = hatk , vec b = 2 hati + (1 - lamda_2 ) hatj + 2hatk , vec c = hati + hatj + (lamda_3 - 2) hatk `
` vecb = 2 veca , " " 1 - lamda_2 = 2 lamda_1 , " " 2 lamda_1 + lamda_2 = 1`
Also , `veca.vec c = 0 rArr 1 + lamda_1 + lamda_3 - 2 = 0`
`lamda_1 + lamda_3 = 1`
hence a possible value of ` (lamda_1, lamda_2,lamda_3) " is " (1/3, 1/3, 2/3)`
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