If vectors P =a i +a j +3 k and Q=a i -2 j - k are perpendicular to each other, then the positive value of a is

Correct answer: A. 3 Vector P =a i +a j +3 k and vector Q =a i -2 j - k . If two vectors are perpendicular to each other, then P · Q =0 or (a i +a j +3 k ) ·(a i -2 j - k )=0 or a^2-2 a-3=0 . Solving this quadratic equation, we get a=3 or -1. Therefore positive value of a is 3.

AIIMS 2002

Exam: AIIMS
Year: 2002
Subject: Physics
Chapter: Mathematics in Physics

AIIMS 2002 · Physics · Mathematics in Physics

If vectors P =a i +a j +3 k and Q=a i -2 j - k are perpendicular to...

If vectors

\vec{P}=a \hat{i}+a \hat{j}+3 \hat{k}

and

Q=a \hat{i}-2 \hat{j}-\hat{k}

are perpendicular to each other, then the positive value of

a

Options

Correct answer

A. 3

Step-by-step solution

Vector

\vec{P}=a \hat{i}+a \hat{j}+3 \hat{k}

and vector

\vec{Q}=a \hat{i}-2 \hat{j}-\hat{k}

. If two vectors are perpendicular to each other, then

\vec{P} \cdot \vec{Q}=0 \quad \text{ or } \quad(a \hat{i}+a \hat{j}+3 \hat{k}) \cdot(a \hat{i}-2 \hat{j}-\hat{k})=0 or

a^2-2 a-3=0

. Solving this quadratic equation, we get

a=3

or -1. Therefore positive value of

is 3.

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