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The diagonals of a parallelogram are the vectors 3i^+6j^-2k^ and -i^-2j^-8k^ then, the length of the shorter side of parallelogram is

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Important Questions on Vector Algebra

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If a and b are unit vectors and angle between them is θ, then sinθ2 is
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If the angle between a and b is 2π3 and the projection of a in the direction of b is -2, then |a|=
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If a and b are mutually perpendicular unit vectors, then 3a+2b·5a-6b=
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A vector a makes equal acute angles on the coordinate axis. Then the projection of vector b=5i^+7j^+k^ on a is
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If a·b=0 and a+b makes an angle 60° with a then 
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If a×b2+a.b2=144 and a=6, then b is equal to
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If |a|=16,|b|=4 then, |a×b|2+|a·b|2=
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A unit vector perpendicular to the plane containing the vectors i^+2j^+k^ and -2i^+j^+3k^ is