Question

The vectors $\overset{\rightarrow}{AB} = 3\mathbf{i} + 4\mathbf{k},$ and $\overset{\rightarrow}{AC} = 5\mathbf{i} - 2\mathbf{j} + 4\mathbf{k}$ are the sides of a triangle ABC. The length of the median through A is

• A. $\sqrt{18}$
• B. $\sqrt{72}$
• C. $\sqrt{33}$
• D. $\sqrt{288}$

Answer 1

Answer: (C)

$\sqrt{33}$

Answer 2

P.V. of $\overset{\rightarrow}{AD} = \frac{(3 + 5)i + (0 - 2)j + (4 + 4)k}{2} = 4\mathbf{i} - \mathbf{j} + 4\mathbf{k}$

$|\overset{\rightarrow}{AD}| = \sqrt{16 + 16 + 1} = \sqrt{33}$.