Question

If $\mathrm{A}^{\rightarrow}=3 \hat{1}+4 \hat{\jmath}+9 \mathrm{k}$ is multiplied by 3 , then the component of the new vector along $\mathrm{z}$ direction is .. (A) $-3$ (B) $+3$ $\begin{array}{ll}\text { (C) }-27 & \text { (D) }+27\end{array}$

Name: Problem 266, Chapter 2: JEE Physics
Uploaded: 2022-01-03T16:15:47-08:00
Duration: 2 min 10 s
Channel: Muhammad Nawaz
Description: If A^→=3 1̂+4 +9 k is multiplied by 3 , then the component of the new vector along z direction is .. (A) -3 (B) +3 (C) -27 (D) +27

    If $\mathrm{A}^{\rightarrow}=3 \hat{1}+4 \hat{\jmath}+9 \mathrm{k}$ is multiplied by 3 , then the component of the new vector along $\mathrm{z}$ direction is ..
(A) $-3$
(B) $+3$ $\begin{array}{ll}\text { (C) }-27 & \text { (D) }+27\end{array}$

JEE Physics

StemEZ 1st Edition

Chapter 2, Problem 266

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Solved by Expert Muhammad Nawaz

01/03/2022

Step 1

Step 1: We are given the vector $\mathrm{A}^{\rightarrow}=3 \hat{i}+4 \hat{j}+9 \hat{k}$ and we are asked to find the component of the new vector along the z direction after multiplying the vector by 3. Show more…

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If $\mathrm{A}^{\rightarrow}=3 \hat{1}+4 \hat{\jmath}+9 \mathrm{k}$ is multiplied by 3 , then the component of the new vector along $\mathrm{z}$ direction is .. (A) $-3$ (B) $+3$ $\begin{array}{ll}\text { (C) }-27 & \text { (D) }+27\end{array}$

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Key Concepts

Scalar Multiplication of Vectors

Scalar multiplication involves multiplying each component of a vector by a constant (the scalar). This operation scales the magnitude of the vector without changing its direction if the scalar is positive. It is fundamental in vector arithmetic and is applied component-wise, meaning that every individual component—whether along the x, y, or z-axis—is multiplied by the scalar.

Vector Components in Cartesian Coordinates

In a Cartesian coordinate system, a vector is expressed in terms of its components along the mutually perpendicular axes (typically x, y, and z). Each component represents the vector's projection or influence in that specific direction. Understanding vector components is essential for performing operations such as addition, subtraction, and scalar multiplication, as well as for analyzing physical quantities in multiple dimensions.

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