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

The projection of point `P( vec p)` on the plane ` vec r. vec n=q ` is `( vec s)` , then a. ` vec s=((q- vec p. vec n) vec n)/(| vec n|^2)` b. ` vec s=p+((q- vec p. vec n) vec n)/(| vec n|^2)` c. ` vec s=p-(( vec p. vec n) vec n)/(| vec n|^2)` d. ` vec s=p-((q- vec p. vec n) vec n)/(| vec n|^2)`

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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