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The projection of point P(vecp) on the p...

The projection of point `P(vecp)` on the plane `vecr.vecn=q` is `(vecs)`, then

A

`vecs=((q-vecp.vecn)vecn)/(|vecn|^(2))`

B

`vecs=vecp+((q-vecp.vecn)vecn)/(|vecn|^(2))`

C

`vecs=vecp-((vecp.vecn)vecn)/(|vecn|^(2))`

D

`vecs=vecp-((q-vecp.vecn)vecn)/(|vecn|^(2))`

Text Solution

Verified by Experts

The correct Answer is:
b
We have `vecs-vecp=lamdavecnandvecs.n=q.` Thus,
`(lamdavecn+vecp).vecn=q`
or `lamda=(q-vecp.vecn)/(|vecn|^(2))`
`impliesvecs=vecp+((vecq-vecp.vecn)vecn)/(|vecn|^(2))`
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CENGAGE-THREE-DIMENSIONAL GEOMETRY -Exercise (Single)
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  9. The co-ordinates of the point P on the line vecr =(hati +hatj + hatk...

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  13. L1a n dL2 and two lines whose vector equations are L1: vec r=lambda((c...

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