Addition and Subtraction in Unit Vector Notation

Q.

Vectors A and B are $6\hat{i}-7\hat{j}+6\hat{k}$ and $3\hat{i}+4\hat{j}+6\hat{k}$ respectively. Their vector difference in unit vector notation will be

1. 9icap -3jcap +12kcap

2. 3icap -11jcap + 0kcap

3. 9icap - 11jcap + 12kcap

4. 10icap -jcap -kcap

Q.

Given both vector A & B have the same magnitude of 1 unit. Find $\overrightarrow{c}$ such that $\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=0$?

1. 

2. 

3. 

4. 

Q.

Add vectors A & D. Which of these is the correct result?

1. 

2. 

3. 

4. None of these

Q.

Find the unit vector in the direction opposite to the direction of the vector $6\hat{i}-8\hat{j}+10\hat{k}$

1. 

2. 

3. None of these.

4. 

Q.

If we add vectors A & E. Which of these is the correct result?

1. 

2. 

3. None of these

4. 

Q.

$\overrightarrow{A}=2\hat{i}+\hat{j},3\hat{j}-\hat{k}$ and $\overrightarrow{C}=6\hat{i}-2\hat{k}$. Value of $\overrightarrow{A}-2\overrightarrow{B}+3\overrightarrow{C}$ would be

1. $20\hat{i}-5\hat{j}+4\hat{k}$

2. $20\hat{i}-5\hat{j}-4\hat{k}$

3. $4\hat{i}+5\hat{j}+20\hat{k}$
   

4. $5\hat{i}+4\hat{j}+10\hat{k}$
   

Q.

The angle between the two vectors $\overrightarrow{A}=3\hat{i}+4\hat{j}+5\hat{k}$ and $\overrightarrow{B}=3\hat{i}+4\hat{j}-5\hat{k}$ will be

1. ${90}^{\circ }$

2. $0^{\circ }$

3. ${60}^{\circ }$

4. ${45}^{\circ }$

Q.

The three vectors $\overrightarrow{A}=3\hat{i}-2\hat{j}+\hat{k},\overrightarrow{B}=\hat{i}-3\hat{j}+5\hat{k}$ and $\overrightarrow{C}=2\hat{i}+\hat{j}-4\hat{k}$ form

1. An equilateral triangle

2. Isosceles triangle

3. A right angled triangle

4. No triangle

Q.

Two forces \(\vec{F_1}=5\hat{i}+10\hat{j}-20\hat{k}\) and $\overrightarrow{F_2}=10\hat{i}-5\hat{j}-20\hat{k}$ act on a single point. The angle between $\overrightarrow{F_1}$ and $\overrightarrow{F_2}$ is nearly

1. ${30}^{\circ }$
   

2. ${45}^{\circ }$
   

3. ${60}^{\circ }$
   

4. ${90}^{\circ }$

Q.

Can we add 2 vectors of unequal magnitudes and get a zero vector?

1. True

2. False