Consider the following statements in respect of a vector d = (a × b) × c: I. d is coplanar with a and b. II. d is perpendicular to c. Which of the statements given above is/are correct?
A.I only
B.II only
C.Both I and II✓ Correct
D.Neither I nor II
Explanation
d = (a×b)×c = (a·c)b - (b·c)a, which is a linear combination of a and b, hence coplanar with a and b. Also d is perpendicular to both (a×b) and c (since cross product result is perpendicular to second factor c). So both statements are correct.
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