Question

If vectors $\overset{\rightarrow}{AB}$= – 3$\overset{\rightarrow}{i}$ + 4$\overset{\rightarrow}{k}$ and $\overset{\rightarrow}{AC}$ = 5 – 2 + 4 are the sides of a DABC, then the length of the median through A is-

• A. $\sqrt{14}$
• B. $\sqrt{18}$
• C. $\sqrt{29}$
• D. 5

Answer 1

Answer: (B)

$\sqrt{18}$

Answer 2

$\overset{\rightarrow}{AB}$+$\overset{\rightarrow}{AC}$ = 2$\overset{\rightarrow}{AD}$

\ $\overset{\rightarrow}{AD}$ = $\frac{1}{2}$ {(–3$\overset{\rightarrow}{i}$+ 4$\overset{\rightarrow}{k}$) + (5$\overset{\rightarrow}{i}$ – 2$\overset{\rightarrow}{j}$ + 4$\overset{\rightarrow}{k}$)}

= ($\overset{\rightarrow}{i}$–$\overset{\rightarrow}{j}$ + 4$\overset{\rightarrow}{k}$)

Length of AD =$\sqrt{1 + 1 + 16}$ = $\sqrt{18}$