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If barb and barc are two non-collinear v...

If `barb` and `barc` are two non-collinear vectors, then number of solutions (x,y) in `x,yin[0,10]` satisfying the equation `baracdot[barb+barc]=5` and `baraxx(barbxxbarc)=(x^(2)-2x+7)barb+(siny)barc` is

A. one
B. Two
C. Zero
D> Infinite

A

one

B

two

C

zero

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
B
`bara xx (barb xx barc) = (bara. ""barc)barb - (bara-barb).barc`
`implies bara-barc =x^2 - 2x + 7, bara .""barb=-siny`
`bara.(barb + barc) = 5`
`implies x^2 - 2x + 7 -siny=5`
`implies (x-1)^2 + 1 = sin y`
`x=1, y=(4n+1) (pi)/(2) = (pi)/(2),(5pi)/(2)`
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