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Question: If \(\mathbf{a} = 2\mathbf{i} + \mathbf{j} - 8\mathbf{k}\) and \(\mathbf{b} = \mathbf{i} + 3\mathbf{...

If a=2i+j−8k\mathbf{a} = 2\mathbf{i} + \mathbf{j} - 8\mathbf{k} and b=i+3j−4k,\mathbf{b} = \mathbf{i} + 3\mathbf{j} - 4\mathbf{k}, then the magnitude of a+b=\mathbf{a} + \mathbf{b} =

A

13

B

133\frac{13}{3}

C

313\frac{3}{13}

D

413\frac{4}{13}

Answer

13

Explanation

Solution

∣a+b∣=∣3i+4j−12k∣=∣32+42+122∣=13|\mathbf{a} + \mathbf{b}| = |3\mathbf{i} + 4\mathbf{j} - 12\mathbf{k}| = |\sqrt{3^{2} + 4^{2} + 12^{2}}| = 13

∴a+b=13\therefore\mathbf{a} + \mathbf{b} = 13.