Question
Check whether the vectors $2 \hat{i}+2 \hat{j}+3 \hat{k}_{+}+-3 \hat{i}+3 \hat{j}+2 \hat{k}_t+3 \hat{i}+4 \hat{k}$ form a triangle or not.
with $\overline{A B}=2 \hat{i}+2 \hat{j}+3 \hat{k}_i \overline{B C}=3 \hat{i}+3 \hat{j}+2 \hat{k}, \overline{A C}=3 \hat{i}+4 \hat{k}$
Now,$\overline{A B}+\overline{B C}$
$=(2 \hat{i}+2 \hat{j}+3 \hat{k})+(-3 \hat{i}+3 \hat{j}+2 \hat{k})$
$=-\hat{i}+5 \hat{j}+5 \hat{k} \neq 3 \hat{i}+4 \hat{k}=\overline{\mathrm{AC}}$
Hence, the three vectors do not form a triangle.
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
In $\triangle \mathrm{ABC}$ if $\sin ^2 \mathrm{~A}+\sin ^2 B=\sin ^2 \mathrm{C}$ then show that the triangle is a right anqled triangle.
$\sqrt{2 x^2+3 x+4}$