Three vectors- A-B and C are such that A-B -0 and A-C -0- then A is collinear to -

Given: A·B =0 ⇒A⊥B Also, nbsp; nbsp; A·C =0 ⇒ A⊥C So, nbsp;A is perpendicular to both nbsp;B and nbsp;nbsp;C. Further, nbsp;nbsp;B× nbsp;C is al ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

Three vectors...

Question

Three vectors, $\to A, \to B$ and $\to C$ are such that $\to A \cdot \to B = 0$ and $\to A \cdot \to C = 0$ , then $\to A$ is collinear to -

\to B

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\to C

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\to A \times \to B

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\to B \times \to C

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Solution

The correct option is D $\to B \times \to C$
Given:

$\to A \cdot \to B = 0 \Rightarrow \to A ⊥ \to B$

Also,

$\to A \cdot \to C = 0 \Rightarrow \to A ⊥ \to C$

So, $\to A$ is perpendicular to both $\to B$ and $\to C$ .

Further, $\to B \times \to C$ is also perpendicular to both $\to B$ and $\to C$ .

$\Rightarrow \to A$ and $\to B \times \to C$ are collinear.

Hence, option $(D)$ is the correct answer.

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Three vectors, →A,→B and →C are such that →A⋅→B=0 and →A⋅→C=0, then →A is collinear to -

The correct option is D →B×→CGiven: →A⋅→B=0 ⇒→A⊥→B Also, →A⋅→C=0⇒ →A⊥→C So, →A is perpendicular to both →B and →C. Further, →B×→C is also perpendicular to both →B and →C. ⇒→A and →B×→C are collinear. Hence, option (D) is the correct answer.

Three vectors, $\to A, \to B$ and $\to C$ are such that $\to A \cdot \to B = 0$ and $\to A \cdot \to C = 0$ , then $\to A$ is collinear to -