First slide

Cross product of vectors or vector product of vectors

Question

If $\vec{a} and \vec{b}$ are any two vectors of magnitudes 2 and 3, respectively, such that $| 2 (\vec{a} \times \vec{b}) | + | 3 (\vec{a} \cdot \vec{b}) | = k$ then the maximum value of k is

Moderate

A

$\sqrt{13}$
B

$2 \sqrt{13}$
C

$6 \sqrt{13}$
D

$10 \sqrt{13}$

Solution

$\begin{array}{l} k = | 2 (\vec{a} \times \vec{b}) | + | 3 (\vec{a} \cdot \vec{b}) | \\ = 12 \sin θ + 18 \cos θ \\ \Rightarrow Maximum value of k = \sqrt{12^{2} + 18^{2}} = 6 \sqrt{13} \end{array}$

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