For what value of $λ$ are the vectors $\vec{a} = 2 \hat{i} + λ \hat{j} + \hat{k} and \vec{b} = \hat{i} - 2 \hat{j} - 3 \hat{k}$ are perpendicular to each other?

Solution

$\vec{a} = 2 \hat{i} + λ \hat{j} + \hat{k} \vec{b} = \hat{i} - 2 \hat{j} + 3 \hat{k} If \vec{a} and \vec{b} are perpendicular to each other, then \vec{a} . \vec{b} must be 0 . \vec{a} . \vec{b} = 2 \hat{i} + λ \hat{j} + \hat{k} . \hat{i} - 2 \hat{j} + 3 \hat{k} 0 = 2 . 1 + λ . (- 2) + 1 . 3 0 = 2 - 2 λ + 3 2 λ = 5 \Rightarrow λ = \frac{5}{2} Thus, the value of λ is \frac{5}{2}$

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Vector Algebra

For what value of $λ$ are the vectors $\vec{a} = 2 \hat{i} + λ \hat{j} + \hat{k} and \vec{b} = \hat{i} - 2 \hat{j} - 3 \hat{k}$ are perpendicular to each other?

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For what value of λ are the vectors a→ = 2i^ + λ j^ + k^ and b→ = i^ - 2j^ -3k^ are perpendicular to each other?

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For what value of $λ$ are the vectors $\vec{a} = 2 \hat{i} + λ \hat{j} + \hat{k} and \vec{b} = \hat{i} - 2 \hat{j} - 3 \hat{k}$ are perpendicular to each other?

Classify the following measures as scalars and vectors.
40 watt

Classify the following measures as scalars and vectors.
10^–19 coulomb

Classify the following measures as scalars and vectors.
20 m/s²

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