The area of the triangle with vertices (1, 2, 0), (1, 0, 2) and (0, 3, 1) in sq. unit is ____. (a) √ 5 (b) √ 7

Question 199 of 215

Q. The area of the triangle with vertices (1, 2, 0), (1, 0, 2) and (0, 3, 1) in sq. unit is ________.

(a)

\sqrt 5

(b)

\sqrt 7

(c)

\sqrt 6

(d)

\sqrt 3

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Area $=\dfrac12|\vec{AB}\times\vec{AC}|$ .

Let $A(1,2,0), B(1,0,2), C(0,3,1)$ .

$\vec{AB}=(0,-2,2)$ , $\vec{AC}=(-1,1,1)$ .

$\vec{AB}\times\vec{AC}=\begin{vmatrix}\hat i&\hat j&\hat k\\0&-2&2\\-1&1&1\end{vmatrix}=(-2-2)\hat i-(0+2)\hat j+(0-2)\hat k=(-4,-2,-2)$

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Q.The area of the triangle with vertices (1, 2, 0), (1, 0, 2) and (0, 3, 1) in sq. unit is ________.