Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 2: Problem 262

The resultant of two vectors \(\mathrm{A}^{\rightarrow}\) and \(\mathrm{B}^{\rightarrow}\) (A) can be smaller than \(\mathrm{A}-\mathrm{B}\) in magnitude (B) can be greater than \(\mathrm{A}+\mathrm{B}\) in magnitude (C) can't be greater than \(\mathrm{A}+\mathrm{B}\) or smaller than \(\mathrm{A}-\mathrm{B}\) in magnitude (D) none of above is true

Short Answer

Expert verified
The correct answer is (D) none of the above is true. Option A and B are both not conclusively proven, while option C is also inconclusive. The relationship between the magnitudes of the vectors may not fully adhere to any of the given options.

Step by step solution

01

(A) Smaller than A - B

: Consider the subtraction of vectors A and B. The resultant vector, say R, can be represented as: \[R = A - B\] Let's represent the magnitude of these vectors as follows: \[|R| = |A - B|\] Here, we need to consider if the magnitude of R can be smaller than the magnitude of A - B. According to the triangle inequality theorem: \[|A - B| \leq |A| + |-B|\] Since the magnitude of a vector is always non-negative, it is true that: \[|A - B| \geq 0\] However, this doesn't answer the question we're trying to address. So, we cannot conclude anything based on this information.
02

(B) Greater than A + B

: Now we will consider if the resultant vector's magnitude can be greater than the sum of the magnitudes of vectors A and B: \[|R| = |A + B|\] According to the triangle inequality theorem: \[|A + B| \leq |A| + |B|\] This implies that the magnitude of the resultant vector cannot be greater than the sum of the magnitudes of vectors A and B. So, option B is incorrect.
03

(C) Can't be greater than A + B or smaller than A - B

: Let's analyze this option by combining the individual results from options A and B. From option B, we already know that the magnitude of the resultant vector cannot be greater than the sum of the magnitudes of vectors A and B: \[|R| \leq |A| + |B|\] Regarding the first part of this statement (can't be smaller than A - B), we cannot make a strong conclusion. So, we will assume it to be inconclusive.
04

(D) None of the above is true

: Since none of the options A, B, and C provides a complete and conclusive answer, we can assume that this statement is correct. It is quite possible that the relationship between the magnitudes of the vectors may not fully adhere to any of the given options. So, we can choose option (D) as the correct answer.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

The resultant of two vectors is maximum when they. (A) are at right angles to each other (B) act in opposite direction (C) act in same direction (D) are act \(120^{\circ}\) to each other

A particle goes from point \(\mathrm{A}\) to \(\mathrm{B}\). Its displacement is \(\mathrm{X}\) and path length is \(\mathrm{y}\). So $\mathrm{x} / \mathrm{y} \ldots$ \((\mathrm{A})>1\) (B) \(<1\) (C) \(\geq 1\) (D) \(\leq 1\)

A particle has initial velocity \((2 \hat{1}+3 \hat{j}) \mathrm{ms}^{-1}\) and has acceleration \((\hat{1}+\hat{j}) \mathrm{ms}^{-2}\). Find the velocity of the particle after 2 second. (A) \((3 \hat{1}+5 \hat{j}) \mathrm{ms}^{-1}\) (B) \((4 \hat{i}+5 \hat{\jmath}) \mathrm{ms}^{-1}\) (C) \((3 \hat{1}+2 \hat{j}) \mathrm{ms}^{-1}\) (D) \((5 \hat{1}+4 \hat{j}) \mathrm{ms}^{-1}\)

Angle of projection of a projectile with horizontal line is \(\theta\) at time \(t=0\), After what time the angle will be again \(\theta\) ? (A) \([(\mathrm{V} \cos \theta) / \mathrm{g}]\) (B) \([(\mathrm{V} \sin \theta) / \mathrm{g}]\) (C) \(\left[\left(\mathrm{V}_{0} \sin \theta\right) / 2 \mathrm{~g}\right]\) (D) \(\left[\left(2 \mathrm{~V}_{0} \sin \theta\right) / \mathrm{g}\right]\)

A freely falling stone crashes through a horizontal glass plate at time \(t\) and losses half of its velocity. After time \((t / 2)\) it falls on the ground. The glass plate is \(60 \mathrm{~m}\) high from the ground. Find the total distance travelled by the stone. \(\left[g=10 \mathrm{~ms}^{-2}\right]\) (A) \(120 \mathrm{~m}\) (B) \(80 \mathrm{~m}\) (C) \(100 \mathrm{~m}\) (D) \(140 \mathrm{~m}\)
See all solutions

Recommended explanations on English Textbooks

Argumentative Essay

Read Explanation

Synthesis Essay

Read Explanation

Language Acquisition

Read Explanation

Lexis and Semantics

Read Explanation

International English

Read Explanation

Essay Prompts

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free