(D) The projection (component) of vector $b$ along vector $a$ is given by the formula: $\text{proj}_a b = (b \cdot \hat{a})\hat{a}$.Since the unit vec

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

$\frac{(a \cdot b)a}{a \cdot a}$

(D) The projection (component) of vector $b$ along vector $a$ is given by the formula: $\text{proj}_a b = (b \cdot \hat{a})\hat{a}$.Since the unit vector $\hat{a} = \frac{a}{|a|}$,we substitute this into the formula:$\text{proj}_a b = \left( b \cdot \frac{a}{|a|} \right) \frac{a}{|a|}$.This simplifies to $\frac{(b \cdot a)a}{|a|^2}$.Since $|a|^2 = a \cdot a$,the expression becomes $\frac{(a \cdot b)a}{a \cdot a}$.

Class 12 Mathematics Vector Algebra Scalar or Dot product of two vectors and its applications

Easy

If $a$ and $b$ are two non-zero vectors,then the component of $b$ along $a$ is

A
$\frac{(a \cdot b)a}{b \cdot b}$
B
$\frac{(a \cdot b)b}{a \cdot a}$
C
$\frac{(a \cdot b)b}{a \cdot b}$
D
$\frac{(a \cdot b)a}{a \cdot a}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Vector Algebra

Subtopic

Scalar or Dot product of two vectors and its applications

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 . . . . . . .

EasyGSEB 2024

View Solution

If $a$ is a vector of magnitude $7$ and $b$ is a vector of magnitude $8$,then the maximum value of $|a \cdot b|$ is:

EasyAP EAMCET 2021

View Solution

The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i + j$ and a vector $b_2$ perpendicular to $a$. Then $b_1 = $

Medium

View Solution

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

Easy

View Solution

If $\vec{a} = -4 \hat{i} + 2 \hat{j} + 4 \hat{k}$ and $\vec{b} = \sqrt{2} \hat{i} - \sqrt{2} \hat{j}$ are two vectors,then the angle between the vectors $2 \vec{a}$ and $\frac{\vec{b}}{2}$ is (in $^{\circ}$)

EasyAP EAMCET 2024

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $a$ and $b$ are two non-zero vectors,then the component of $b$ along $a$ is

Similar Questions

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 . . . . . . .

If $a$ is a vector of magnitude $7$ and $b$ is a vector of magnitude $8$,then the maximum value of $|a \cdot b|$ is:

The vector $b = 3j + 4k$ is to be written as the sum of a vector $b_1$ parallel to $a = i + j$ and a vector $b_2$ perpendicular to $a$. Then $b_1 = $

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

If $\vec{a} = -4 \hat{i} + 2 \hat{j} + 4 \hat{k}$ and $\vec{b} = \sqrt{2} \hat{i} - \sqrt{2} \hat{j}$ are two vectors,then the angle between the vectors $2 \vec{a}$ and $\frac{\vec{b}}{2}$ is (in $^{\circ}$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module