First slide

Scalars and Vectors

Question

In vectors A and B be respectively equal to $3 \hat{i} - 4 \hat{j} + 5 \hat{k}$ $and 2 \hat{i} + 3 \hat{j} - 4 \hat{k} .$ The unit vector parallel to A + B is $\frac{1}{\sqrt{27}} (5 \hat{i} - \hat{a j} + \hat{k})$ The value of a is ________

Moderate

Solution

$\vec{A} + \vec{B} = 5 \hat{i} - \hat{j} + \hat{k} \Rightarrow U n i t V e c t o r = \frac{1}{\sqrt{27}} (5 \hat{i} - \hat{j} + \hat{k}) \Rightarrow a = 1$

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