If a, b and c are three vectors such that a t | vedclass

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

Question

(C) Given that $a, b$ and $c$ are mutually perpendicular vectors such that $a 	imes b = c$ and $b 	imes c = a$.Since the vectors are mutually perpen

Vedclass · Accepted Answer

$1$ only

Vedclass · Answer

(C) Given that $a, b$ and $c$ are mutually perpendicular vectors such that $a 	imes b = c$ and $b 	imes c = a$.Since the vectors are mutually perpendicular,we have $a \cdot b = 0$,$b \cdot c = 0$,and $c \cdot a = 0$.Also,the magnitude of the cross product is given by $|a 	imes b| = |a||b| \sin(90^\circ) = |a||b| = |c|$.Similarly,$|b 	imes c| = |b||c| = |a|$.Substituting $|a| = |b||c|$ into the first equation: $|b||c| \cdot |b| = |c|$.Since $c$ is a vector,$|c| 
eq 0$,so we can divide by $|c|$ to get $|b|^2 = 1$.Since the magnitude $|b|$ must be non-negative,$|b| = 1$.

If $a, b$ and $c$ are three vectors such that $a \times b = c$,$b \times c = a$ and $a, b, c$ are mutually perpendicular to each other,then $|b|$ is equal to

Similar Questions

The number of unit vectors perpendicular to $\overline{a}=(1,1,0)$ and $\overline{b}=(0,1,1)$ is

$A$ unit vector perpendicular to both $i+j+k$ and $2i+j+3k$ is

The area of a parallelogram whose adjacent sides are given by the vectors $i + 2j + 3k$ and $-3i - 2j + k$ (in square units) is

If $a=2\hat{i}+\hat{j}-3\hat{k}$,$b=\hat{i}-2\hat{j}+\hat{k}$,$c=-\hat{i}+\hat{j}-4\hat{k}$ and $d=\hat{i}+\hat{j}+\hat{k}$,then $|(a \times b) \times(c \times d)|=$

Let $\vec{a} = 2\hat{i} + 3\hat{j} + 3\hat{k}$ and $\vec{b} = 6\hat{i} + 3\hat{j} + 3\hat{k}$. Then the square of the area of the triangle with adjacent sides determined by the vectors $(2\vec{a} + 3\vec{b})$ and $(\vec{a} - \vec{b})$ is :

Vedclass Test Series

Exam Paper Generator

Online Exam Module