Question 100: Motion in 2D & Vectors

Question

Given $\quad \vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k}), \quad \vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k})$ and $\vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k}) \cdot(\vec{A}+\vec{B}) \cdot \vec{C}$ will be

Accepted Answer

WeÃ¢ÂÂre asked to compute something involving vectors:
$ \vec{A} = (2\hat{i} - 3\hat{j} + \hat{k}), \quad  \vec{B} = (3\hat{i} + \hat{j} - 2\hat{k}), \quad  \vec{C} = (3\hat{i} + 2\hat{j} + \hat{k}). $
Expression: $(\vec{A}+\vec{B}) \cdot \vec{C}$.
Step 1. Add A and B:
$ \vec{A}+\vec{B} = (2+3)\hat{i} + (-3+1)\hat{j} + (1 - 2)\hat{k} = 5\hat{i} - 2\hat{j} - \hat{k}. $
So $\vec{A}+\vec{B} = (5, -2, -1).$
$\vec{C} = (3, 2, 1).$
Step 2. Dot product:
$ (\vec{A}+\vec{B}) \cdot \vec{C} = (5)(3) + (-2)(2) + (-1)(1)  = 15 - 4 - 1  = 10. $
Ã¢ÂÂ Final Answer:
$ (\vec{A}+\vec{B}) \cdot \vec{C} = 10 $
So the correct option is
A. 10
.

Answer

10

Answer

12 c

Answer

18

Answer

20

Motion in 2D & Vectors

Given \quad \vec{A}=(2 \hat{i}-3 \hat{j}+\hat{k}), \quad \vec{B}=(3 \hat{i}+\hat{j}-2 \hat{k}) and \vec{C}=(3 \hat{i}+2 \hat{j}+\hat{k}) \cdot(\vec{A}+\vec{B}) \cdot \vec{C} will be

Choose the correct answer: