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## Q. 1.1

Calculate the magnitudes of the vectors (a) (2, 2); (b) (2, 2$\sqrt{3}$); (c) (-2$\sqrt{3}$, 2); (d) (-3, – 3); (e) (6, -6).

## Verified Solution

$|\mathbf{v}|=\text { magnitude of } \mathbf{v}=\sqrt{a^{2}+b^{2}}$

(a) $|\mathbf{v}|=\sqrt{2^{2}+2^{2}}=\sqrt{8}=2 \sqrt{2}$
(b) $|\mathbf{v}|=\sqrt{2^{2}+(2 \sqrt{3})^{2}}=4$
(c) $|\mathbf{v}|=\sqrt{(-2 \sqrt{3})^{2}+2^{2}}=4$
(d) $|\mathbf{v}|=\sqrt{(-3)^{2}+(-3)^{2}}=\sqrt{18}=3 \sqrt{2}$
(e) $|\mathbf{v}|=\sqrt{6^{2}+(-6)^{2}}=\sqrt{72}=6 \sqrt{2}$