Find a unit vector perpendicular to each of the vector $\vec{a} + \vec{b} and \vec{a} - \vec{b}$ , where
$\vec{a} = 3 \hat{i} + 2 \hat{j} + 2 \hat{k} and \vec{b} = \hat{i} + 2 \hat{j} - 2 \hat{k} .$

Solution

$\vec{a} = 3 \hat{i} + 2 \hat{j} + 2 \hat{k}, \vec{b} = \hat{i} + 2 \hat{j} - 2 \hat{k} . ∴ \vec{a} + \vec{b} = 4 \hat{i} + 4 \hat{j} and \vec{a} - \vec{b} = 2 \hat{i} + 4 \hat{k} (\vec{a} + \vec{b}) x (\vec{a} - \vec{b}) = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 4 & 4 & 0 \\ 2 & 0 & 4 \end{matrix}| = \hat{i} (16) - \hat{j} (16) + \hat{k} (- 8) = 16 \hat{i} - 16 \hat{j} - 8 \hat{k} ∴ |(\vec{a} + \vec{b}) x (\vec{a} - \vec{b})| = \sqrt{16^{2} + (- 16)^{2} + 64} = \sqrt{256 + 256 + 64} = \sqrt{576} = 24$

So, the unit vector, perpendicular to each of the vectors $\vec{a} + \vec{b} and \vec{a} + \vec{b}$ is given by

$\pm \frac{(\vec{a} + \vec{b}) x (\vec{a} - \vec{b})}{|(\vec{a} + \vec{b}) x (\vec{a} - \vec{b})|} = \pm \frac{16 \hat{i} - 16 \hat{j} - 8 \hat{k}}{24} = \pm \frac{2 \hat{i} - 2 \hat{j} - \hat{k}}{3} = \pm \frac{2 \hat{i}}{3} \mp \frac{2}{3} \hat{j} \mp \frac{1}{3} \hat{k}$

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Vector Algebra

Find a unit vector perpendicular to each of the vector $\vec{a} + \vec{b} and \vec{a} - \vec{b}$ , where
$\vec{a} = 3 \hat{i} + 2 \hat{j} + 2 \hat{k} and \vec{b} = \hat{i} + 2 \hat{j} - 2 \hat{k} .$

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Vector Algebra

Find a unit vector perpendicular to each of the vector a→ + b→ and a→ - b→ , where a→ = 3 i^ + 2 j^ + 2 k^ and b→ = i^ + 2 j^ - 2 k^.

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Find a unit vector perpendicular to each of the vector $\vec{a} + \vec{b} and \vec{a} - \vec{b}$ , where
$\vec{a} = 3 \hat{i} + 2 \hat{j} + 2 \hat{k} and \vec{b} = \hat{i} + 2 \hat{j} - 2 \hat{k} .$

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.
velocity

Classify the following measures as scalars and vectors.
work done