Let vec{a}, vec{b}, vec{c} be the position ve | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The area of a triangle with vertices having position vectors $\vec{a}, \vec{b}, \vec{c}$ is given by the formula: Area $= \frac{1}{2} |\vec{AB}

Vedclass · Accepted Answer

$\frac{1}{2} |\vec{a} 	imes \vec{b} + \vec{b} 	imes \vec{c} + \vec{c} 	imes \vec{a}|$

Vedclass · Answer

(C) The area of a triangle with vertices having position vectors $\vec{a}, \vec{b}, \vec{c}$ is given by the formula: Area $= \frac{1}{2} |\vec{AB} 	imes \vec{AC}|$. Here,$\vec{AB} = \vec{b} - \vec{a}$ and $\vec{AC} = \vec{c} - \vec{a}$. Substituting these into the formula: Area $= \frac{1}{2} |(\vec{b} - \vec{a}) 	imes (\vec{c} - \vec{a})|$. Expanding the cross product: $(\vec{b} - \vec{a}) 	imes (\vec{c} - \vec{a}) = \vec{b} 	imes \vec{c} - \vec{b} 	imes \vec{a} - \vec{a} 	imes \vec{c} + \vec{a} 	imes \vec{a}$. Since $\vec{a} 	imes \vec{a} = 0$,$-\vec{b} 	imes \vec{a} = \vec{a} 	imes \vec{b}$,and $-\vec{a} 	imes \vec{c} = \vec{c} 	imes \vec{a}$,we get: Area $= \frac{1}{2} |\vec{a} 	imes \vec{b} + \vec{b} 	imes \vec{c} + \vec{c} 	imes \vec{a}|$. Thus,the correct option is $C$.

Let $\vec{a}, \vec{b}, \vec{c}$ be the position vectors of the vertices $A, B, C$ of a triangle respectively. Find the area of the triangle.

Similar Questions

Let $A=(3,4,0), B=(4,4,4), C=(-6,2,3)$ and $D=(1,1,2)$. If $\theta$ is the acute angle between the lines $AB$ and $CD$,then $\cos \theta=$

If the moduli of $a$ and $b$ are equal and the angle between them is $120^\circ$ and $a \cdot b = -8$,then $|a|$ is equal to

If $\bar{a}, \bar{b}, \bar{c}, \bar{d}$ are the position vectors of the points $A, B, C, D$ respectively such that $3 \bar{a}-\bar{b}+2 \bar{c}-4 \bar{d}=\overline{0}$,then the position vector of the point of intersection of the line segments $AC$ and $BD$ is

If two vectors $\vec{a}$ and $\vec{b}$ which are perpendicular to each other are such that $|\vec{a}|=8$ and $|\vec{b}|=3$,then $|\vec{a}-2\vec{b}|=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module