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Multiplication with Vectors

Assertion: A×...

Question

Assertion: $\to A \times \to B$ is perpendicular to both $\to A + \to B$ as well as $\to A - \to B .$
Reason: $\to A + \to B$ as well as $\to A - \to B$ lie in the plane containing $\to A$ and $\to B$ but $\to A \times \to B$ lies perpendicular to the plane containing $\to A$ and $\to B .$

A

If both assertion and reason are true and the reason is the correct explanation of the assertion.

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B

If both assertion and reason are true but reason is not the correct explanation of the assertion.

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C

If assertion is true but reason is false.

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D

If the assertion and reason both are false.

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E

If assertion is false but reason is true.

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Solution

The correct option is A If both assertion and reason are true and the reason is the correct explanation of the assertion.
Cross product of two vectors is perpendicular to the plane containing both the vectors.

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Similar questions

\to A \times \to B

is perpendicular to both

\to A + \to B

\to A - \to B .

\to A + \to B

\to A - \to B

lie in the plane containing

\to A

\to B

\to A \times \to B

lies perpendicular to the plane containing

\to A

\to B .

Q. In the relationship

\to A \times \to B = \to C

. which statement is true?

Q. A vector perpendicular to both vector

\to A =^i + 2^j +^k

\to B =^i +^j -^k

In figure, AP and BQ are perpendiculars to the line segment AB and AP = BQ. Prove that O is the midpoint of line segment AB as well as PQ.

Two vectors $\to A$ and $\to B$ lie in a plane, another vector $\to C$ lies outside this plane, then the resultant of these three vectors i.e., $\to A + \to B + \to C$

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