(D) Given,$|a| = 7$ and $|b| = 8$. The dot product of two vectors is given by $a \cdot b = |a||b| \cos \theta$,where $\theta$ is the angle between the

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

$56$ and the angle between them is $0$ or $\pi$

(D) Given,$|a| = 7$ and $|b| = 8$. The dot product of two vectors is given by $a \cdot b = |a||b| \cos \theta$,where $\theta$ is the angle between the vectors. Taking the magnitude on both sides,we get $|a \cdot b| = |a||b| |\cos \theta|$. Substituting the given values,$|a \cdot b| = 7 \times 8 |\cos \theta| = 56 |\cos \theta|$. The maximum value of $|\cos \theta|$ is $1$,which occurs when $\theta = 0$ or $\theta = \pi$. Therefore,the maximum value of $|a \cdot b|$ is $56 \times 1 = 56$.

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

Easy

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:

AP EAMCET 2021 All AP EAMCET

A
$56$ and the angle between them is $\frac{\pi}{6}$
B
$56$ and the angle between them is $\frac{\pi}{3}$
C
$56$ and the angle between them is $\frac{\pi}{2}$
D
$56$ and the angle between them is $0$ or $\pi$

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

Previous Year

AP EAMCET 2021 Paper All AP EAMCET years →

Let $\vec{u}$ be a vector coplanar with the vectors $\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{b} = \hat{j} + \hat{k}$. If $\vec{u}$ is perpendicular to $\vec{a}$ and $\vec{u} \cdot \vec{b} = 24$,then $|\vec{u}|^2 = \dots$

DifficultJEE MAIN 2018

View Solution

If $3\vec{a} - 5\vec{b}$ and $2\vec{a} + \vec{b}$ are perpendicular to each other,and $\vec{a} + 4\vec{b}$ and $-\vec{a} + \vec{b}$ are also perpendicular to each other,and $\theta$ is the angle between $\vec{a}$ and $\vec{b}$,then find $\cos \theta$.

Difficult

View Solution

If $|a| = 3, |b| = 4, |c| = 5$ and $a + b + c = 0,$ then the angle between $a$ and $b$ is

Easy

View Solution

If $\vec{\lambda}$ is a unit vector perpendicular to the plane of vectors $\vec{a}$ and $\vec{b}$,and the angle between them is $\theta$,then $\vec{a} \cdot \vec{b}$ will be:

Medium

View Solution

If $a=\hat{i}+\hat{j}+t \hat{k}$ and $b=\hat{i}+2 \hat{j}+3 \hat{k}$,then the values of $t$ for which $(a+b)$ and $(a-b)$ are perpendicular are:

MediumAP EAMCET 2001

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

Similar Questions

Let $\vec{u}$ be a vector coplanar with the vectors $\vec{a} = 2\hat{i} + 3\hat{j} - \hat{k}$ and $\vec{b} = \hat{j} + \hat{k}$. If $\vec{u}$ is perpendicular to $\vec{a}$ and $\vec{u} \cdot \vec{b} = 24$,then $|\vec{u}|^2 = \dots$

If $3\vec{a} - 5\vec{b}$ and $2\vec{a} + \vec{b}$ are perpendicular to each other,and $\vec{a} + 4\vec{b}$ and $-\vec{a} + \vec{b}$ are also perpendicular to each other,and $\theta$ is the angle between $\vec{a}$ and $\vec{b}$,then find $\cos \theta$.

If $|a| = 3, |b| = 4, |c| = 5$ and $a + b + c = 0,$ then the angle between $a$ and $b$ is

If $\vec{\lambda}$ is a unit vector perpendicular to the plane of vectors $\vec{a}$ and $\vec{b}$,and the angle between them is $\theta$,then $\vec{a} \cdot \vec{b}$ will be:

If $a=\hat{i}+\hat{j}+t \hat{k}$ and $b=\hat{i}+2 \hat{j}+3 \hat{k}$,then the values of $t$ for which $(a+b)$ and $(a-b)$ are perpendicular are:

Vedclass Test Series

Exam Paper Generator

Online Exam Module