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The vectors a and b are not perpendicular and c and d are two vectors satisfying b×c = b×d and a·d = 0. Then the vector d is equal to

1. c + ((a·c)/(a·b)) b
2. b + ((b·c)/(a·b)) c
3. c - ((a·c)/(a·b)) b
4. b - ((b·c)/(a·b)) c

Correct answer: c - ((a·c)/(a·b)) b

Solution

The correct option is derived from the condition that the cross products of b with c and d are equal, indicating that d can be expressed as a linear combination of c and a vector in the direction of b. The term ((a·c)/(a·b)) b adjusts c by projecting it onto the direction of b, ensuring that d remains orthogonal to a, as required by the condition a·d = 0.

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