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Question

If r.^i=r.^j=r.^k and |r|=2, then find r.

A
2(^i+^j+^k)
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B
23(^i+^j+^k)
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C
23(^i+^j+^k)
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D
3(^i+^j+^k)
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Solution

The correct option is C 23(^i+^j+^k)
Let r=x^i+y^j+z^k.

Scalar product of a vector with a unit vector of x, y and z axis gives us the magnitude of vector in x, y and z direction i.e. the value of x, y and z.

Since, r.^i=r.^j=r.^kx=y=z(i)
Also,
|r|=2=x2+y2+z2=x2+x2+x23x2=23x=2x=23

Hence the required vector,
r=23(^i+^j+^k)

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