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Three vectors vecP,vecQ " and " vecR are...

Three vectors `vecP,vecQ " and " vecR` are shown in the figure. Let S be any point on the vector `vecR`. The distance between the points P and S is `b|vecR|`. The general relation among vectors` vecP,vecQ " and " vecS` is:

A

`vecS=(b-1)vecP+bvecQ`

B

`vecS=(1-b^(2))vecP+bvecQ`

C

`vecS=(1-b)vecP+b^(2)vecQ`

D

`vecS=(1-b)vecP+vecQ`

Text Solution

Verified by Experts

The correct Answer is:
D
(d): Let vector `vec S` represent the position vector for the point S. Then we can write the following:
`vecS=vecP+b vecR=vecP+b(vecQ-vecP)=vecP(1-b)+b vecQ`
Hence, option (d) is correct .
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