Question

The $(x, y, z)$ co-ordinates of two points $A$ and $B$ are given respectively as $(0,3,-1)$ and $(-2,6,4)$. The displacement vector from $A$ to $B$ is given by (A) $-2 \hat{i}+6 \hat{j}+4 \hat{k}$ (B) $-2 \hat{i}+3 \hat{j}+3 \hat{k}$ (C) $-2 \hat{i}+3 \hat{j}+5 \hat{k}$ (D) $2 \hat{i}-3 \hat{j}-5 \hat{k}$

Name: Problem 39, Chapter 1: A Complete Resource Book in Physics for JEE Main
Uploaded: 2021-10-07T00:26:35-08:00
Duration: 1 min 37 s
Channel: Akshaya Rs
Description: The (x, y, z) co-ordinates of two points A and B are given respectively as (0,3,-1) and (-2,6,4). The displacement vector from A to B is given by (A) -2 î+6 ĵ+4 k̂ (B) -2 î+3 ĵ+3 k̂ (C) -2 î+3 ĵ+5 k̂ (D) 2 î-3 ĵ-5 k̂

   The $(x, y, z)$ co-ordinates of two points $A$ and $B$ are given respectively as $(0,3,-1)$ and $(-2,6,4)$. The displacement vector from $A$ to $B$ is given by
(A) $-2 \hat{i}+6 \hat{j}+4 \hat{k}$
(B) $-2 \hat{i}+3 \hat{j}+3 \hat{k}$
(C) $-2 \hat{i}+3 \hat{j}+5 \hat{k}$
(D) $2 \hat{i}-3 \hat{j}-5 \hat{k}$

A Complete Resource Book in Physics for JEE Main

Sanjeev Kumar 1st Edition

Chapter 1, Problem 39

Instant Answer

Solved by Expert Akshaya Rs

10/07/2021

Step 1

The position vector for a point is simply a vector that starts at the origin and ends at the point. So, for point A, the position vector is $0\hat{i} + 3\hat{j} - 1\hat{k}$ and for point B, the position vector is $-2\hat{i} + 6\hat{j} + 4\hat{k}$. Show more…

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The $(x, y, z)$ co-ordinates of two points $A$ and $B$ are given respectively as $(0,3,-1)$ and $(-2,6,4)$. The displacement vector from $A$ to $B$ is given by (A) $-2 \hat{i}+6 \hat{j}+4 \hat{k}$ (B) $-2 \hat{i}+3 \hat{j}+3 \hat{k}$ (C) $-2 \hat{i}+3 \hat{j}+5 \hat{k}$ (D) $2 \hat{i}-3 \hat{j}-5 \hat{k}$

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Key Concepts

3D Cartesian Coordinates

This concept refers to the system of specifying points in three-dimensional space using the (x, y, z) components. It forms the basis for describing locations of points and objects in space, which is essential in geometry, physics, and engineering.

Displacement Vector

A displacement vector represents the change in position of an object and is defined as the difference between the final and initial position vectors. In problems involving points in 3D space, the displacement vector is calculated by subtracting each corresponding coordinate of the initial point from the final point.

Vector Subtraction

Vector subtraction involves subtracting corresponding components of one vector from another. In the context of finding displacement, it helps determine the direction and magnitude from one point to another by computing the difference between their coordinate values.

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