Let in a $ riangle ABC$, the length of the side $AC$ be $6$, the vertex $B$ be $(1,2,3)$ and the vertices $A,C$ lie on the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$. Then the area (in sq. units) of $ riangle ABC$ is:

Question

Let in a $	riangle ABC$, the length of the side $AC$ be $6$, the vertex $B$ be $(1,2,3)$ and the vertices $A,C$ lie on the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$. Then the area (in sq. units) of $	riangle ABC$ is:

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] The line passes through $P(6,7,7)$ with direction $\vec d=(3,2,-2)$, $|\vec d|=\sqrt{17}$. $\vec{BP}=(5,5,4)$ and $\vec{BP}	imes\vec d=(-18,22,-5)$, whose magnitude is $\sqrt{833}=7\sqrt{17}$. So the distance from $B$ to the line (the height) is $7$. Area $=\frac12\cdot6\cdot7=21$. Answer (2).

Q. Let in a $\triangle ABC$, the length of the side $AC$ be $6$, the vertex $B$ be $(1,2,3)$ and the vertices $A,C$ lie on the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$. Then the area (in sq. units) of $\triangle ABC$ is:

Explanation

Reviewed by Dr. Abubacker

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