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If a X b= c X d and a X c= b X d then the vectors a-d and b-c are: a)non-collinear b)linearly independent c)perpendicular d)parallal Please explain how to approach these type of quesions

If a X b= c X d and a X c= b X d then the vectors a-d and b-c are:
a)non-collinear
b)linearly independent
c)perpendicular
d)parallal
Please explain how to approach these type of quesions

Grade:12th pass

1 Answers

Riddhish Bhalodia
askIITians Faculty 434 Points
5 years ago
subtracting the two we have
a \times (b-c) = (c-b) \times d = - (b - c) \times d = d \times (b-c)
hence
(a-d) \times (b-c) = 0
hence for such a situation to occur the vectors a-d and b-c are parallal

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