Find the angle between the vectors $\vec{a} = \hat{i} - \hat{j} + \hat{k} and \vec{b} = \hat{1} + \hat{j} - \hat{k}$

Solution

$\vec{a} = \hat{i} - \hat{j} + \hat{k} \vec{b} = \hat{i} + \hat{j} - \hat{k} Now, \vec{a} . \vec{b} = |\vec{a}| |\vec{b}| cosθ Where θ is the angle between \vec{a} and \vec{b}; also 0 \leq θ \leq π \hat{i} - \hat{j} + \hat{k} . \hat{i} + \hat{j} - \hat{k} = (\sqrt{1^{1} + (- 1)^{2} + 1^{2}}) (\sqrt{1^{1} + (- 1)^{2} + 1^{2}}) cosθ [1 . 1 + (- 1) . 1 + 1 . (- 1)] = [\sqrt{3} . \sqrt{3} cosθ] 1 - 1 - 1 = 3 cosθ - 1 = 3 cosθ cosθ = \frac{- 1}{3} \Rightarrow θ = \cos^{- 1} (\frac{- 1}{3})$

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Find the angle between the vectors $\vec{a} = \hat{i} - \hat{j} + \hat{k} and \vec{b} = \hat{1} + \hat{j} - \hat{k}$

Classify the following measures as scalars and vectors.
40°

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.
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Classify the following measures as scalars and vectors.
work done