If A - B - C - D- then select the correct alternative-A- A is perpendicular to CB- Component of C along A - component of D along AC- B is parallel to C - DD- Component of C- along A- - component of D- along A-

The correct option is D Component of C⃗ along A⃗= component of D⃗ along A⃗ According to definition of cross product C⃗+D⃗ is perpendicular to both A⃗ and B⃗ ...

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Byju's Answer

Standard XII

Mathematics

Test for Collinearity of Vectors

If A × B = C ...

Question

If $\to A \times \to B = \to C + \to D$ , then select the correct alternative:

$\to B$ is parallel to $\to C + \to D$

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$\to A$ is perpendicular to $\to C$

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Component of $\to C$ along $\to A =$ component of $\to D$ along $\to A$

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Component of $\to C$ along $\to A =$ - component of $\to D$ along $\to A$

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Solution

The correct option is D
Component of $\to C$ along $\to A =$ - component of $\to D$ along $\to A$

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

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If→A×→B=→C+→D, then select the correct alternative:

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