Write the value of p for which $\vec{a} = 3 \hat{i} + 2 \hat{j} + 9 \hat{k} and \vec{b} = \hat{i} + p \hat{j} + 3 \hat{k}$ are parallel vectors.

Solution

Two vectors $\vec{a} and \vec{b}$ are parallel

$\vec{a} = 3 \hat{i} + 2 \hat{j} + 9 \hat{k} and \vec{b} = \hat{i} + p \hat{j} + 3 \hat{k} \vec{a} = λ \vec{b} So 3 \hat{i} + 2 \hat{j} + 9 \hat{k} = λ (\hat{i} + p \hat{j} + 3 \hat{k}) \Rightarrow 3 \hat{i} + 2 \hat{j} + 9 \hat{k} = λ \hat{i} + p λ \hat{j} + 3 λ \hat{k} \Rightarrow λ = 3, p λ = 2 and 9 = 3 λ \Rightarrow p = \frac{2}{3}$

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Vector Algebra

Write the value of p for which $\vec{a} = 3 \hat{i} + 2 \hat{j} + 9 \hat{k} and \vec{b} = \hat{i} + p \hat{j} + 3 \hat{k}$ are parallel vectors.

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Write the value of p for which a→ = 3i^ + 2j^ + 9k^ and b→ = i^+pj^ +3k^ are parallel vectors.

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Classify the following measures as scalars and vectors.time period

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Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Write the value of p for which $\vec{a} = 3 \hat{i} + 2 \hat{j} + 9 \hat{k} and \vec{b} = \hat{i} + p \hat{j} + 3 \hat{k}$ are parallel vectors.

Classify the following measures as scalars and vectors.
time period

Classify the following measures as scalars and vectors.
distance

Classify the following measures as scalars and vectors.
force

Classify the following measures as scalars and vectors.
velocity

Classify the following measures as scalars and vectors.
work done