/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 39 The \((x, y, z)\) co-ordinates o... [FREE SOLUTION] | 91影视

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Chapter 1: Problem 39

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) \(2 \hat{i}-3 \hat{j}-5 \hat{k}\)

Short Answer

Expert verified
The correct option for the displacement vector from point A to point B is (C): \(\vec{AB} = -2 \hat{i} + 3 \hat{j} + 5 \hat{k}\).

Step by step solution

01

Write down the coordinates of points A and B

Given, point A has coordinates \((0, 3, -1)\) and point B has coordinates \((-2, 6, 4)\).
02

Calculate the displacement vector from A to B

The formula to find the displacement vector from point A to point B is given by: \[ \vec{AB} = (x_2 - x_1) \hat{i} + (y_2 - y_1) \hat{j} + (z_2 - z_1) \hat{k} \] Using the coordinates of A and B, plug in the values: \[ \vec{AB} = (-2 - 0) \hat{i} + (6 - 3) \hat{j} + (4 - (-1)) \hat{k} \]
03

Simplify the displacement vector

Simplifying the vector, we get: \[ \vec{AB} = -2 \hat{i} + 3 \hat{j} + 5 \hat{k} \]
04

Find the correct option

Comparing our computed displacement vector with the given options, we can see that our answer matches with option (C): \[ \vec{AB} = -2 \hat{i} + 3 \hat{j} + 5 \hat{k} \] So, the correct option for the displacement vector from point A to point B is (C).

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