First slide

Scalars and Vectors

Question

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

Difficult

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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