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

If $\overrightarrow{a} \cdot \hat{i} = \overrightarrow{a} \cdot (2 \hat{i} + \hat{j}) = \overrightarrow{a} \cdot (\hat{i} + \hat{j} + 3 \hat{k}) = 1$,then $\overrightarrow{a}$ is equal to :

If $a, b, c$ are unit vectors such that $a + b + c = 0,$ then $a \cdot b + b \cdot c + c \cdot a = $

For non-zero vectors $a$ and $b$,if $|a+b| < |a-b|$,then $a$ and $b$ are

If the area of a parallelogram whose diagonals are represented by vectors $\vec{d_1} = 3 \hat{i} + \lambda \hat{j} + 2 \hat{k}$ and $\vec{d_2} = \hat{i} - 2 \hat{j} + 3 \hat{k}$ is $\frac{\sqrt{117}}{2}$ sq. units,then $\lambda=$

Let $a = 2i + j + k$ and $b = i + 2j - k$. If a unit vector $c$ is coplanar with $a$ and $b$,and $c$ is perpendicular to $a$,then $c$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module