If a neq 0, b neq 0 and |a + b| = |a - b|, th | vedclass

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

Question

(B) Given that $|a + b| = |a - b|$.Squaring both sides,we get $|a + b|^2 = |a - b|^2$.Using the property $|x|^2 = x \cdot x$,we have $(a + b) \cdot (a

Vedclass · Accepted Answer

Perpendicular to each other

Vedclass · Answer

(B) Given that $|a + b| = |a - b|$.Squaring both sides,we get $|a + b|^2 = |a - b|^2$.Using the property $|x|^2 = x \cdot x$,we have $(a + b) \cdot (a + b) = (a - b) \cdot (a - b)$.Expanding the dot product,we get $a \cdot a + 2(a \cdot b) + b \cdot b = a \cdot a - 2(a \cdot b) + b \cdot b$.Subtracting $a \cdot a + b \cdot b$ from both sides,we get $2(a \cdot b) = -2(a \cdot b)$.This implies $4(a \cdot b) = 0$,which means $a \cdot b = 0$.Since the dot product of two non-zero vectors is zero,the vectors $a$ and $b$ are perpendicular to each other.

If $a \neq 0, b \neq 0$ and $|a + b| = |a - b|,$ then the vectors $a$ and $b$ are

Similar Questions

The work done by the force $F = 2i - 3j + 2k$ in displacing a particle from the point $(3, 4, 5)$ to the point $(1, 2, 3)$ is ............ $unit$.

If $\hat{a}$ is a unit vector such that $(\bar{x}-\hat{a}) \cdot (\bar{x}+\hat{a}) = 8$,then $|\bar{x}| = $

If $a = x^2 \hat{i} + x \hat{j} + 3 \hat{k}$ and $b = x \hat{i} - 4 \hat{j} + 2 \hat{k}$ and $a \cdot b > 6$,then:

The projection of vector $\vec{a} = \hat{i} + 2\hat{j} + \hat{k}$ on vector $\vec{b} = 2\hat{i} + 3\hat{j} + 2\hat{k}$ is . . . . . . .

Vedclass Test Series

Exam Paper Generator

Online Exam Module