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Question

Vector a has components ax=3,ay=4. The componenets of a vector c which is perpendicular to a and has a magnitude of 5 units will be

A
cx=4, cy=3
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B
cx=4, cy=3
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C
cx=4, cy=3
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D
Both (a) and (b)
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Solution

The correct option is D Both (a) and (b)
a=3^i+4^j
Let c=cx^i+cy^j
Asc is perpendicular to a
c.a=0
3cx+4cy=0
cy=34cx ...(i)

We know |c|=5,
Thus, c2x+c2y=25
c2x+9c2x16=25
cx=±4 and from equation (i), cy=3.

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