(A) Given vectors are $a = 2i + j - 8k$ and $b = i + 3j - 4k$.First,calculate the sum of the vectors $a + b$:$a + b = (2i + i) + (j + 3j) + (-8k - 4k)

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

(A) Given vectors are $a = 2i + j - 8k$ and $b = i + 3j - 4k$.First,calculate the sum of the vectors $a + b$:$a + b = (2i + i) + (j + 3j) + (-8k - 4k) = 3i + 4j - 12k$.Now,find the magnitude of the resulting vector $|a + b|$:$|a + b| = \sqrt{(3)^2 + (4)^2 + (-12)^2}$$|a + b| = \sqrt{9 + 16 + 144}$$|a + b| = \sqrt{169}$$|a + b| = 13$.Thus,the magnitude of $a + b$ is $13$.

Class 12 Mathematics Vector Algebra Basic , Modulus and Algebra of vectors

Easy

If $a = 2i + j - 8k$ and $b = i + 3j - 4k,$ then the magnitude of $a + b = $

A
$13$
B
$\frac{13}{3}$
C
$\frac{3}{13}$
D
$\frac{4}{13}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Vector Algebra

Subtopic

Basic , Modulus and Algebra of vectors

If $C$ is the mid-point of the line segment $AB$ and $P$ is any point outside the line $AB$,then

EasyAP EAMCET 2022

View Solution

If one side of a square is represented by the vector $3i + 4j + 5k,$ then the area of the square is

Easy

View Solution

Let $a = i$ be a vector which makes an angle of $120^\circ$ with a unit vector $b$. Then the unit vector $(a + b)$ is

Easy

View Solution

$a$ and $b$ are two non-collinear vectors,then $xa + yb$ (where $x$ and $y$ are scalars) represents a vector which is

Medium

View Solution

$A$ unit vector which is in the opposite direction of $(2, -2, 1)$ is $........$

Medium

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 $a = 2i + j - 8k$ and $b = i + 3j - 4k,$ then the magnitude of $a + b = $

Similar Questions

If $C$ is the mid-point of the line segment $AB$ and $P$ is any point outside the line $AB$,then

If one side of a square is represented by the vector $3i + 4j + 5k,$ then the area of the square is

Let $a = i$ be a vector which makes an angle of $120^\circ$ with a unit vector $b$. Then the unit vector $(a + b)$ is

$a$ and $b$ are two non-collinear vectors,then $xa + yb$ (where $x$ and $y$ are scalars) represents a vector which is

$A$ unit vector which is in the opposite direction of $(2, -2, 1)$ is $........$

Vedclass Test Series

Exam Paper Generator

Online Exam Module