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The vectors which is/are coplanar with v...

The vectors which is/are coplanar with vectors `hati+hatj+2hatk and hati+2hatj+hatk` and perpendicular to the vector `hati+hatj+hatk ` is /are (A) `hatj-hatk` (B) `-hati+hatj` (C) `hati-hatj` (D) `-hatj+hatk`

A

`(2hati + hatj - 3hatk)/(sqrt14)`

B

`(hatj + hatk)/(sqrt2)`

C

`(hati - hatj)/(sqrt(2))`

D

`(hati - hatk)/(sqrt(2))`

Text Solution

Verified by Experts

The correct Answer is:
B
Let the unit vector be `ahati + bhatj + c hatk` then `|(a,b,c),(1,1,2),(1,2,1)| = 0, a + b + c = 0 and a^2 + b^2 + c^2 = 1`
`-3a + b + c = 0, a + b + c = 0 implies a = 0 and b = c`
`implies b^2 = 1/2 implies "Vector is" 1/(sqrt2) hatj - 1/(sqrt(2))hatk or (-1)/(sqrt(2)) hatj + 1/(sqrt(2)) hatk`.
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