If |a| = 2,|b| = 3 and a, b are mutually perp | vedclass

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

Question

(C) Let the vertices of the triangle be $O(0)$,$A(a + b)$,and $B(a - b)$.The area of the triangle is given by $\frac{1}{2} |\vec{OA} 	imes \vec{OB}|$

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(C) Let the vertices of the triangle be $O(0)$,$A(a + b)$,and $B(a - b)$.The area of the triangle is given by $\frac{1}{2} |\vec{OA} 	imes \vec{OB}|$.Substituting the vectors,we get $	ext{Area} = \frac{1}{2} |(a + b) 	imes (a - b)|$.Expanding the cross product: $(a + b) 	imes (a - b) = a 	imes a - a 	imes b + b 	imes a - b 	imes b$.Since $a 	imes a = 0$ and $b 	imes b = 0$,and $b 	imes a = -(a 	imes b)$,we have:$(a + b) 	imes (a - b) = 0 - (a 	imes b) - (a 	imes b) - 0 = -2(a 	imes b) = 2(b 	imes a)$.Thus,$	ext{Area} = \frac{1}{2} |2(b 	imes a)| = |b 	imes a| = |b| |a| \sin(90^\circ)$.Given $|a| = 2$ and $|b| = 3$,and the vectors are perpendicular $(	heta = 90^\circ)$:$	ext{Area} = 3 	imes 2 	imes 1 = 6$.

If $|a| = 2$,$|b| = 3$ and $a, b$ are mutually perpendicular,then the area of the triangle whose vertices are $0, a + b, a - b$ is

Similar Questions

In Young's double slit experiment,the wavelength of red light is $7800 \, \mathring{A}$ and that of blue light is $5200 \, \mathring{A}$. The value of $n$ for which the $n^{th}$ bright band due to red light coincides with the $(n + 1)^{th}$ bright band due to blue light is:

$A$ particle of mass $5 \times 10^{-5} \ kg$ is placed at the lowest point of a smooth parabola $x^2 = 40y$ (where $x$ and $y$ are in $m$). If it is displaced slightly such that it is constrained to move along the parabola,the angular frequency of oscillation (in $rad/s$) will be approximately:

An unpolarised light is incident at an interface of two dielectric media having refractive indices of $2$ (incident medium) and $2 \sqrt{3}$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is . . . . . . .

Hot concentrated sulphuric acid,on reaction with which one of the following elements,produces two gaseous products?

Match the following and choose the correct answer:-
$(A)$ Implantation $(i)$ Vagina
$(B)$ Capacitation (ii) Ovary
$(C)$ Folliculogenesis (iii) Uterus
$(D)$ Fertilisation (iv) Fallopian tube

Vedclass Test Series

Exam Paper Generator

Online Exam Module