Question

The two vectors j + k and 3i – j + 4k represent the two sides ab and ac, respectively of a triangle abc. Find the length of the median through a

Answer 1

Solution:

$\vec {AB} = \hat j + \hat k \\ \\ \vec {AC} = 3 \hat i - \hat j + 4 \hat k$

So,using Triangle law of vector addition

$\vec{BC} = \vec{AC} - \vec{AB} \\ \\ = (3 \hat i - \hat j + 4 \hat k) - ( \hat j + \hat k) \\ \\ \vec{BC} = 3 \hat i - 2 \hat j + 3 \hat k$
Since AD is median,so it bisect the side,s o

$BD = \frac{1}{2} BC \\ \\ = \frac{3}{2} \hat i - \hat j + \frac{3}{2}\hat k$

Now again using Triangle law of vector addition

$\vec{AD} = \vec{AB} + \vec{BD} \\ \\ = ( \hat j + \hat k)+(\frac{3}{2} \hat i - \hat j + \frac{3}{2}\hat k) \\ \\ \vec {AD} = \frac{3}{2} \hat i + 0\hat j + \frac{5}{2}\hat k$

To find the length of the median AD,find the magnitude of vector AD
$= \sqrt{{(\frac{3}{2})}^{2}+0^{2}+{(\frac{5}{2})}^{2}}\\\\AD=\frac{1}{2}\sqrt{34}\:units$

Answer 2

Answer:

I hope it will help uh

ok....