Multiplication with Vectors

Q.

What is the angle between the following pair vectors? $\overrightarrow{A}=\hat{i}+\hat{j}+\hat{k}and\overrightarrow{B}=-2\hat{i}-2\hat{j}-2\hat{k}$

1. ${60}^{\circ }$

2. ${30}^{\circ }$

3. ${90}^{\circ }$

4. ${180}^{\circ }$

Q. What happens if a vector is multiplied by a number – 2?

1. The magnitude of the vector is doubled but its direction remains the same
2. The magnitude of the vector remains the same but its direction is reversed
3. The magnitude of the vector is doubled and its direction is reversed
4. Neither the magnitude nor the direction of the vector undergo any change

Q.

Calculate the area of the triangle determined by the two vectors $\overrightarrow{A}=3\hat{i}+4\hat{j}and\overrightarrow{B}=-3\hat{i}+7\hat{j}$

1. $0squnit$

2. $20squnit$

3. $16.5squnit$

4. $12.4squnit$

Q.

What happens if a vector is multiplied by the number 2?

1. The magnitude of the vector is doubled but its direction remains the same.

2. The magnitude of the vector remains the same but its direction is reversed.

3. The magnitude of the vector is doubled and its direction is reversed.

4. Neither the magnitude nor the direction of the vector undergo any change.

Q.

What happens if a vector is multiplied by the number -2?

1. The magnitude of the vector is doubled and its direction is reversed.

2. The magnitude of the vector remains the same but its direction is reversed.

3. Neither the magnitude nor the direction of the vector undergo any change.

4. The magnitude of the vector is doubled but its direction remains the same.

Q.

What is the angle between the following pair vectors? $\overrightarrow{A}=\hat{i}+\hat{j}+\hat{k}and\overrightarrow{B}=-2\hat{i}-2\hat{j}-2\hat{k}$

1. ${60}^{\circ }$

2. ${30}^{\circ }$

3. ${90}^{\circ }$

4. ${180}^{\circ }$

Q. The resultant of $\overrightarrow{P}$ and $\overrightarrow{Q}$ is perpendicular to $\overrightarrow{P}$. What is the angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$.

1. 
2. 
3. 
4. 

Q. Vertices of a triangle are represented by vectors $\overrightarrow{A}=\hat{i}-2\hat{j}+2\hat{k},\overrightarrow{B}=2\hat{i}+\hat{j}-\hat{k}$ and $\overrightarrow{C}=3\hat{i}-\hat{j}+2\hat{k}$. Then,

1. Length of side AB is 5 units.
2. Length of side BC is of length $\sqrt{14}$ units.
3. Angle between side AB & BC is $\theta =co{s}^{-1}\sqrt{\frac{14}{19}}$.
4. Angle between side AB and BC is ${30}^{\circ }$.

Q. If $\overrightarrow{a}=3\hat{i}+4\hat{j}$ and $\overrightarrow{b}=2\hat{i}-3\hat{j}$ then, $(\overrightarrow{a}+\overrightarrow{b}).(\overrightarrow{a}-\overrightarrow{b})$ is?

1. 8
2. 5
3. 12
4. 0

Q. If $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ are unit vectors then, $|\overrightarrow{a}-\overrightarrow{b}{|}^2+|\overrightarrow{b}-\overrightarrow{c}{|}^2+|\overrightarrow{c}-\overrightarrow{a}{|}^2$ can take the value of

1. 3
2. 5
3. 12
4. 8