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Question: The position vectors of A and B are \(2\mathbf{i} - 9\mathbf{j} - 4\mathbf{k}\) and \(6\mathbf{i} - ...

The position vectors of A and B are 2i−9j−4k2\mathbf{i} - 9\mathbf{j} - 4\mathbf{k} and 6i−3j+8k6\mathbf{i} - 3\mathbf{j} + 8\mathbf{k} respectively, then the magnitude of AB→\overset{\rightarrow}{AB} is

A

11

B

12

C

13

D

14

Answer

14

Explanation

Solution

AB→=(6−2)i+(−3+9)j+(8+4)k=4i+6j+12k\overset{\rightarrow}{AB} = (6 - 2)i + ( - 3 + 9)j + (8 + 4)k = 4i + 6j + 12k

∣AB→∣=16+36+144=14.|\overset{\rightarrow}{AB}| = \sqrt{16 + 36 + 144} = 14.