Question:
Given two vectors $ A\to =-\widehat{i}+2\widehat{j}-3\widehat{k} $ and $ B\to =4\widehat{i}+2\widehat{j}-6\widehat{k}. $ . The angle made by $ (A\to +B\to ) $ with x-axis is
Given two vectors $ A\to =-\widehat{i}+2\widehat{j}-3\widehat{k} $ and $ B\to =4\widehat{i}+2\widehat{j}-6\widehat{k}. $ . The angle made by $ (A\to +B\to ) $ with x-axis is
Updated On: Aug 15, 2024
- $ 30{}^\circ $
- $ 45{}^\circ $
- $ 60{}^\circ $
- $ 90{}^\circ $
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The Correct Option is B
Solution and Explanation
Given, $ \vec{A}=-\hat{i}+2\hat{j}-3\hat{k} $ $ \hat{B}=4\hat{i}-2\hat{j}+6\hat{k} $ Let angle made by $ (\vec{A}+\vec{B}) $ with $ x- $ axis is $ \theta . $ $ \cos \theta =\frac{(\vec{A}+\vec{B}).\hat{i}}{|\vec{A}+\vec{B}|.|\hat{i}|}=\frac{(3\hat{i}+3\hat{k}).\hat{i}}{\sqrt{9+9}.1} $ $ =\frac{3}{3\sqrt{2}}=\frac{1}{\sqrt{2}} $ $ \therefore $ $ \theta ={{45}^{o}} $
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Concepts Used:
Vector Basics
What is a Vector Quantity?
Vector Quantity is a physical quantity that is specified not only by its magnitude but also by its direction. A vector quantity whose magnitude is equal to one and has direction is called a unit vector.
Examples of vector quantity are-
- Displacement
- Linear momentum
- Momentum
- Acceleration
- Force
- Electric field
- Angular velocity
- Polarization