The angle between two vectors $$a=4i^+7j^+6k^$$ and $$b=3i^+3j^$$−$$c10k^$$ is π$$3rad$$. The value of $$3c17$$ is $$____________$$

a⋅$$b=$$|a||b|$$cos$$⁡θ or $$12+21$$−$$6c10=16+49+36$$×$$9+9+c2100$$×$$12$$∴$$c=17$$∴$$3c17=3$$×$$1717=3$$

Scalars and Vectors

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The angle between two vectors $a = 4 \hat{i} + 7 \hat{j} + 6 \hat{k}$ $and b = 3 \hat{i} + 3 \hat{j} - \frac{c}{10} \hat{k} is \frac{π}{3} rad . The value of \frac{3 c}{17} is$ ____________

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Solution

$\begin{array}{l} a \cdot b = | a | | b | \cos θ \\ or 12 + 21 - \frac{6 c}{10} = \sqrt{16 + 49 + 36} \times \sqrt{9 + 9 + \frac{c^{2}}{100}} \times \frac{1}{2} \end{array}$
$\begin{array}{l} ∴ c = 17 \\ ∴ \frac{3 c}{17} = \frac{3 \times 17}{17} = 3 \end{array}$

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