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Q.

If $\vec{A}, \vec{B}, \vec{C} a n d \vec{D}$ are four non-zero vectors in the same plane no two of which are collinear then which of the following hold(s) good?

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a

$(\vec{A} \times \vec{B}) . (\vec{C} \times \vec{D}) = 0$

b

$(\vec{A} \times \vec{C}) . (\vec{B} \times \vec{D}) \neq 0$

c

$(\vec{A} \times \vec{B}) \times (\vec{C} \times \vec{D}) = 0$

d

$(\vec{A} \times \vec{C}) \times (\vec{B} \times \vec{D}) \neq 0$

answer is B, C.

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Detailed Solution

Obviously (b) and (c).

$\bar{A} \times \bar{C} a n d \vec{B} \times \vec{D}$ are both perpendicular to the same plane.

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If A→,B→,C→ and D→ are four non-zero vectors in the same plane no two of which are collinear then which of the following hold(s) good?