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Chapter 2: Problem 256

\(\mathrm{P}^{\rightarrow}=\mathrm{Q}^{\rightarrow}\) is true, if \(\ldots\) (A) their magnitudes are equal (B) they are in same direction (C) their magnitudes are equal and they are in same direction (D) their magnitudes are not equal and they are not in same direction

Short Answer

Expert verified
Vectors \(\mathrm{P}^{\rightarrow}\) and \(\mathrm{Q}^{\rightarrow}\) are equal if their magnitudes are equal and they are in the same direction.

Step by step solution

01

Understanding Vector Equality

Two vectors are considered equal if and only if both their magnitudes (length) and directions are equal. This means that if two vectors have the same length and point in the same direction, they are equal.
02

Analyzing the Given Statements

We will now analyze the given statements based on the condition of vector equality we discussed in Step 1. (A) their magnitudes are equal - If only magnitudes are equal but the direction is not, the vectors are not equal. (B) they are in the same direction - If they have the same direction but different magnitudes, they are not equal. (C) their magnitudes are equal and they are in the same direction - This statement satisfies the condition of vector equality we mentioned in Step 1. (D) their magnitudes are not equal and they are not in the same direction - If both magnitudes and direction are not equal, they are definitely not equal vectors.
03

Choosing the Correct Statement

Based on our analysis in Step 2, we can conclude that statement (C) is the correct one. Vectors \(\mathrm{P}^{\rightarrow}\) and \(\mathrm{Q}^{\rightarrow}\) are equal if their magnitudes are equal and they are in the same direction.

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Most popular questions from this chapter

Which from the following is true? (A) $\cos \theta=\left[\left(\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|\right) / \mathrm{AB}\right]$ (B) $\sin \theta=\left[\left(\mathrm{A}^{\rightarrow} \cdot \mathrm{B}^{\rightarrow}\right) / \mathrm{AB}\right]$ (C) $\tan \theta=\left[\left(\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|\right) /\left(\mathrm{A}^{-}-\mathrm{B}^{-}\right)\right]$ (D) $\cot \theta=\left[\mathrm{AB} /\left(\left|\mathrm{A}^{\rightarrow} \times \mathrm{B}^{\rightarrow}\right|\right)\right]$

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