Question 101: Motion in 2D & Vectors

Question

A unit vector in the direction of resultant vector of $\vec{A}=-2 \hat{i}+3 \hat{j}+\hat{k}$ and $\vec{B}=\hat{i}+2 \hat{j}-4 \hat{k}$ is

Accepted Answer

We are asked:
A unit vector in the direction of the resultant vector of
$ \vec{A} = -2\hat{i} + 3 \hat{j} + \hat{k}, \quad \vec{B} = \hat{i} + 2 \hat{j} - 4 \hat{k}. $
Step 1: Find the resultant
$ \vec{R} = \vec{A} + \vec{B}  = (-2 + 1)\hat{i} + (3+2)\hat{j} + (1 - 4)\hat{k} = (-1)\hat{i} + 5 \hat{j} - 3 \hat{k}. $
So,
$ \vec{R} = -\hat{i} + 5 \hat{j} - 3 \hat{k}. $
Step 2: Magnitude of $\vec{R}$
$ |\vec{R}| = \sqrt{(-1)^2 + 5^2 + (-3)^2}  = \sqrt{1 + 25 + 9}  = \sqrt{35}. $
Step 3: Unit vector in the direction of $\vec{R}$
$ \hat{R} = \frac{\vec{R}}{|\vec{R}|}  = \frac{-\hat{i} + 5\hat{j} - 3\hat{k}}{\sqrt{35}}. $
Ã¢ÂÂ Final Answer:
Option D
$ \frac{-\hat{i} + 5\hat{j} - 3\hat{k}}{\sqrt{35}} $

Answer

$\frac{-3 \hat{\mathrm{i}}+\hat{\mathrm{j}}+5 \hat{\mathrm{k}}}{\sqrt{35}}$

Answer

$\frac{\hat{i}+2 \hat{j}-4 \hat{k}}{\sqrt{35}}$

Answer

$\frac{-2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}}}{\sqrt{35}}$

Answer

$\frac{-\hat{\mathrm{i}}+5 \hat{\mathrm{j}}-3 \hat{\mathrm{k}}}{\sqrt{35}}$

Motion in 2D & Vectors

A unit vector in the direction of resultant vector of \vec{A}=-2 \hat{i}+3 \hat{j}+\hat{k} and \vec{B}=\hat{i}+2 \hat{j}-4 \hat{k} is

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