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Q.

a→ and b→ are two given vectors. On these vectors as adjacent sides, a parallelogram  is constructed. The vector which is the altitude of the parallelogram and perpendicular  to a→ is given by:

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a

a→ ⋅ b→|a→|2   a→ − b→

b

a→ ⋅ b→|b→|2   b→ − a→

c

b→ × (a→ × b→)|b→|2

d

a→ ⋅ b→|a→|2  a→ + b→

answer is A.

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Detailed Solution

The altitude required is BN→BN→=ON→−OB→= projection of OB→ on ON→−b→=   (b→ ⋅ a∧) a∧ − b→=  b→ ⋅ a→|a→| a→|a→|  − b→ =  (b→ ⋅a→) a→|a→|2  − b→
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a→ and b→ are two given vectors. On these vectors as adjacent sides, a parallelogram  is constructed. The vector which is the altitude of the parallelogram and perpendicular  to a→ is given by: