First slide

Vectors

Question

$If \vec{A} \times \vec{B} = \vec{C} + \vec{D}, then select the correct alternative .$

Difficult

A

$\vec{B} is parallel to \vec{C} + \vec{D}$
B

$\vec{A} is perpendicular to \vec{C}$
C

Component of $\overset{\leftarrow}{C} along \vec{A} = component of \vec{D} along \vec{A}$
D

$\overset{\leftarrow}{C} along \vec{A} = - component of \vec{D} along \vec{A}$

Solution

According to definition of cross - product $\vec{C} + \vec{D}$ is perpendicular to both $\vec{A} and \vec{B}$ .
i.e., $\vec{A} . (\vec{C} + \vec{D}) = 0$
$or \vec{A} . \vec{C} + \vec{A} . \vec{D} = 0$
or (component of $\vec{C} along \vec{A}) + (component of \vec{D} along \vec{A}) = 0$
or component of $\vec{C} along \vec{A}) = - (component of \vec{D} along \vec{A})$

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