Question

Area of the triangle whose two sides = 2i - 3j + k, = i - j + 2k is

(a) (b) 1/2

(c) 2 (d) None of these
​

Answer 1

Answer:

Area of triangle is$\frac{\sqrt{35}}{2}$square units

Step-by-step explanation:

Given:

$\vec{a}= 2\vec{i}-3\vec{j}+\vec{k}$

$\vec{b}=\vec{i} - \vec{j }+2\vec{k}$

$\vec{a}*\vec{b}=\left|\begin{array}{ccc}\vec{i}&\vec{j}&\vec{k}\\2&-3&1\\1&-1&2\end{array}\right|$

$\implies\:\vec{a}*\vec{b}=(-6+1)\vec{i}-(4-1)\vec{j}+(-2+3)\vec{k}$

$\implies\:\vec{a}*\vec{b}=-5\vec{i}-3\vec{j}+\vec{k}$

$\implies\:|\vec{a}*\vec{b}|=\sqrt{(-5)^2+(-3)^2+1^2}$

$\implies\:|\vec{a}*\vec{b}|=\sqrt{25+9+1}$

$\implies\:|\vec{a}*\vec{b}|=\sqrt{35}$

Now,

Area of triangle

$=\frac{1}{2}|a*b|$

$=\frac{1}{2}\sqrt{35}$square units