Assertion : If dot product and cross product of P and Q are zero, it implies that one of the vector P and Q must be null vector. Reason : A null vector is a vector of zero magnitude.

Correct answer: B. If both assertion and reason are true but reason is not the correct explanation of assertion. As per question, | A · B |=| A × B |=0 This is possible if either A=0 or B=0 . Magnitude of a null vector is zero.

AIIMS 201827 May

Exam: AIIMS
Year: 2018
Date: 27 May
Subject: Physics
Chapter: Mathematics in Physics

AIIMS 2018 · 27 May · Physics · Mathematics in Physics

Assertion : If dot product and cross product of P and Q are zero,...

Assertion : If dot product and cross product of

\vec{P}

and

\vec{Q}

are zero, it implies that one of the vector

\vec{P}

and

\vec{Q}

must be null vector. Reason : A null vector is a vector of zero magnitude.

Options

AIf both assertion and reason are true and reason is the correct explanation of assertion.
BIf both assertion and reason are true but reason is not the correct explanation of assertion.
CIf assertion is true but reason is false.
DIf both assertion and reason are false.

Correct answer

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

Step-by-step solution

As per question,

|\vec{A} \cdot \vec{B}|=|\vec{A} \times \vec{B}|=0

This is possible if either

A=0

B=0

. Magnitude of a null vector is zero.

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