Let a, b, c be the position vectors of the ve | vedclass

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

Question

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

Vedclass · Accepted Answer

$\frac{1}{2}(a 	imes b + b 	imes c + c 	imes a)$

Vedclass · Answer

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

Let $a, b, c$ be the position vectors of the vertices of a triangle $ABC$. The vector area of triangle $ABC$ is

Similar Questions

If $\bar{a}=\hat{i}-2 \hat{j}+3 \hat{k}$ and $\bar{b}=2 \hat{i}+3 \hat{j}-\hat{k}$,then the angle between the vectors $(2 \bar{a}+\bar{b})$ and $(\bar{a}+2 \bar{b})$ is

Find a unit vector in the $xy$-plane which makes an angle of $45^{\circ}$ with the vector $i + j$ and an angle of $60^{\circ}$ with the vector $3i - 4j$.

Find the angle between two vectors $\vec{a}$ and $\vec{b}$ with magnitudes $1$ and $2$ respectively,given that $\vec{a} \cdot \vec{b} = 1$.

Let $\vec{a}$ and $\vec{b}$ be two unit vectors. If the vectors $\vec{c} = \vec{a} + 2\vec{b}$ and $\vec{d} = 5\vec{a} - 4\vec{b}$ are perpendicular to each other,then the angle between $\vec{a}$ and $\vec{b}$ is:

Let $\vec{a}, \vec{b}, \vec{c}$ be $3$ vectors such that $|\vec{a}|=3, |\vec{b}|=2\sqrt{2}, |\vec{c}|=5$ and $\vec{c}$ is perpendicular to the plane of $\vec{a}$ and $\vec{b}$. If the angle between the vectors $\vec{a}$ and $\vec{b}$ is $\frac{\pi}{4}$, then $|\vec{a}+\vec{b}+\vec{c}|=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module