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Question

The magnitude of the projection of 2^i+3^j+4^k on the vector ^i+^j+^k will be –––


A

3

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B

32

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C

33

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D

None of the above

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Solution

The correct option is C

33


Let a and b be the two vectors as shown

The projection of b along a will beOA=bcosθ=b(a.b|a|b) (cosθ=a.b|a|b)=a.b|a|So magnitude of projection of 2^i+3^j+4^k on ^i+^j+^k will be(2^i+3^j+4^k).^i+^j+^k3=23+33+43=93=33 units


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