What vector must be added to the sum of two vectors 2 𝐢̂-𝐣̂+3 𝐤̂ and 3 𝐢̂-2 𝐣̂-2 𝐤̂ so that the

Name: Problem 29, Chapter 3: Master Resource Book in JEE Main Physics
Uploaded: 2022-01-21T15:41:14-08:00
Duration: 1 min 56 s
Channel: Dheeraj Sharma
Description: What vector must be added to the sum of two vectors 2 𝐢̂-𝐣̂+3 𝐤̂ and 3 𝐢̂-2 𝐣̂-2 𝐤̂ so that the resultant is a unit vector along Z-axis? (a) 5 𝐢̂+k̂ (b) -5 î+3 ĵ (c) 3 ĵ+5 k̂ (d) -3 ĵ+2 k̂

step 1 In this question we have to find that what vector must be added to the sum of the two vectors so

Question

What vector must be added to the sum of two vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ so that the resultant is a unit vector along $Z$-axis? (a) $5 \hat{\mathbf{i}}+\hat{\mathrm{k}}$ (b) $-5 \hat{i}+3 \hat{j}$ (c) $3 \hat{j}+5 \hat{k}$ (d) $-3 \hat{j}+2 \hat{\mathrm{k}}$

   What vector must be added to the sum of two vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ so that the resultant is a unit vector along $Z$-axis?
(a) $5 \hat{\mathbf{i}}+\hat{\mathrm{k}}$
(b) $-5 \hat{i}+3 \hat{j}$
(c) $3 \hat{j}+5 \hat{k}$
(d) $-3 \hat{j}+2 \hat{\mathrm{k}}$

Master Resource Book in JEE Main Physics

D. B. Singh 1st Edition

Chapter 3, Problem 29

Instant Answer

Solved by Expert Dheeraj Sharma

01/21/2022

Step 1

We are asked to find a vector $\vec{R}$ such that the sum of $\vec{P}$, $\vec{Q}$, and $\vec{R}$ is a unit vector along the $Z$-axis, which we can denote as $\hat{k}$. Show more…

Show all steps

Thanks for your feedback!

What vector must be added to the sum of two vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ so that the resultant is a unit vector along $Z$-axis? (a) $5 \hat{\mathbf{i}}+\hat{\mathrm{k}}$ (b) $-5 \hat{i}+3 \hat{j}$ (c) $3 \hat{j}+5 \hat{k}$ (d) $-3 \hat{j}+2 \hat{\mathrm{k}}$

Play audio

Feedback

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Vector Addition

Vector addition involves summing corresponding components of vectors to produce a new vector. In three-dimensional space, when adding vectors, you add the i, j, and k components separately to obtain the resultant vector.

Component-wise Equation Setup

When a condition is given for a resultant vector, such as being a specific unit vector along an axis, you must equate each corresponding component of the sum to the target vector. This process results in individual equations for each component (i, j, and k) that allow you to solve for any unknown vector components.

Unit Vector

A unit vector has a magnitude of 1 and indicates direction only. In problems where a unit vector is required, particularly along coordinate axes, it means that the resultant vector must have specific components that yield the appropriate magnitude and direction, such as (0, 0, 1) for a unit vector in the Z direction.

Please give Ace some feedback