Two vectors ` hat j + hat k` and ` 3 hat i - hat j + 4 hat k` represents the two side vectors ` vec AB and vec AC` respectively of `Delta ABC` Find the length of median from A.

Explanation

`\vec{A B}=\hat{j}+\hat{k} \quad \vec{A C}=3 \hat{i}-\hat{j}+4 \hat{k}`


`\vec{B D}=\frac{1}{2} \vec{B C}`


According to law in triangle ABC `\quad\{\vec{C B}=-\vec{B C}\}`


`\vec{A C}+\vec{C B}=\vec{A B}`


`\vec{A C}-\vec{B C}=\vec{A B}`

`\vec{B C}=\vec{A C}-\vec{A B}=3 \hat{i}-\hat{j}+4 \hat{k}-\hat{j}-\hat{k}`





`\vec{B C}=3 \hat{i}-2 \hat{j}+3 \hat{k}`

`\vec{D B} =\frac{1}{2}(3 \hat{\i}-2 \hat{\j}+3 \hat{k})`

In triangle ABD `\vec{A B}=\vec{A D}+\vec{D B}`

`\vec{A B}=\vec{A D}-\vec{B D}`

`\vec{A D}=\vec{A B}+\vec{B D}=\hat{j}+\hat{k}+\frac{3}{2} \hat{i}-\hat{j}+\frac{3}{2} \hat{k}`

=`\frac{3}{2} \hat{\i}+\frac{5}{2} \hat{k}`

`|\vec{A D}|=\sqrt(\frac{3}{2}\)^{2}+\sqrt(\frac{5}{2})^{2})`

=`\sqrt{\frac{9}{4}+\frac{25}{4}}=\sqrt{8cdot5} \text { units }`