Mathematics

Problem

The length of longer diagonal of the parallelogram constructed on

5\mathbf{a}+2\mathbf{b}

and

\mathbf{a}-3\mathbf{b}

, when it is given that

|\mathbf{a}|=2\sqrt{2}

|\mathbf{b}|=3

and angle between

\mathbf{a}

and

\mathbf{b}

\frac{\pi}{4}

, is a. 15 b.

\sqrt{113}

\sqrt{593}

\sqrt{369}

Intuitive explanation

When you construct a parallelogram from two vectors as adjacent sides, the diagonals are their sum and difference. Here, you need to find both diagonals of the parallelogram with sides $5\mathbf{a}+2\mathbf{b}$ and $\mathbf{a}-3\mathbf{b}$ , then identify which is longer by computing their magnitudes using the dot product formula $|\mathbf{v}|^2 = \mathbf{v} \cdot \mathbf{v}$ .

Intuitive explanation

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