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Which of the following is/are the points...

Which of the following is/are the points that is/are at a distance of 12 units from the point whose position vector is `(8hatk+10hatj-8hatk)` on the line which is parallel to `(2hati+hatj+2hatk)`?

A

`16hati+14hatj`

B

`6hatj-16hatk`

C

`(16hati+18hatj-4hatk)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, B
Line through `8hati+10hatj-8hatk` and parallel to `2hati+hatj+2hatk` is
`vecr=(8hati+10hatj-8hatk)+t(2hati+hatj+2hatk)`
`therefore vecr-(8hati+10hatj-8hatk)=t(2hati+hatj+2hatk)`
`therefore |vecr-(8hati+10hatj-8hatk)|=3|t|`
`therefore 12=+-t.3 rArr t=+-4`
`vecr-(18hati+10hatj-8hatk)=+-4(2hati+hatj+2hatk)`
`vecr=16hati+14hatj` or `vecr=6hatj-16hatk`
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