If the vectors AB=3 i+4 k and AC=5 i-2 j+4 k are the sides of a triangle ABC, then the len…

Question

If the vectors $\overrightarrow{AB}=3\hat i+4\hat k$ and $\overrightarrow{AC}=5\hat i-2\hat j+4\hat k$ are the sides of a triangle $ABC$, then the length of the median through $A$ is:

Accepted Answer

The median from $A$ goes to the midpoint $M$ of $BC$: $\overrightarrow{AM}=\dfrac{\overrightarrow{AB}+\overrightarrow{AC}}2 = \dfrac{8\hat i-2\hat j+8\hat k}2 = 4\hat i-\hat j+4\hat k$

$$|\overrightarrow{AM}|=\sqrt{16+1+16}=\sqrt{33}$$

Solutions · 1