Negative of a Vector

Q. Define negative of a vector.

Q. The negative of vector $2\hat{i}-3\hat{j}$ is

1. $2\hat{i}+3\hat{j}$
2. $2\hat{i}-3\hat{j}$
3. $-2\hat{i}-3\hat{j}$
4. $3\hat{j}-2\hat{i}$

Q. Which is true about a negative of a vector?

1. A vector is negative when it is multiplied by a negative coefficient.
2. None of the above
3. A vector is negative if it is of the different magnitude of the given vector but acts in a direction opposite to that of the given vector.
4. A negative vector is a vector which points in the direction opposite to the reference positive direction.

Q.

A car has a velocity $\overrightarrow{v}=80km/hr$ towards east. Another car on the road has a velocity = $\overrightarrow{-v}$. The magnitude and direction of velocity of second car is

1. 80 km/hr towards south
2. 80 km/hr towards west
3. Direction cannot be determined from the given information
4. Speed of the second car cannot be determined from the given information.

Q. Refer to the following figure and find the option(s) with correct descriptions about the vectors given in the figure.

1. =
2. =
3. =
4. =

Q.

A car has a velocity $\overrightarrow{v}=80km/hr$ towards east. Another car on the road has a velocity = . $\overrightarrow{-v}$The speed and the direction of vecthe second car is

a) 80 km/hr towards south

b) 80 km/hr towards west

c) Direction cannot be determined from the given information

d) Speed of the second car cannot be determined from the given information.

1. 80 km/hr towards south
2. Direction cannot be determined from the given information
3. 80 km/hr towards west
4. Speed of the second car cannot be determined from the given information.

Q.

A car has a velocity $\overrightarrow{v}=80km/hr$ towards east. Another car on the road has a velocity = $\overrightarrow{-v}$. The magnitude and direction of velocity of second car is

1. 80 km/hr towards west
2. 80 km/hr towards south
3. Direction cannot be determined from the given information
4. Speed of the second car cannot be determined from the given information.

Q. Refer to the following figure and find the option(s) with correct descriptions about the vectors given in the figure.

1. $\underset{a}{\to }$ = $\underset{-b}{\to }$
2. $\underset{a}{\to }$ = $\underset{-c}{\to }$
3. $\underset{c}{\to }$ = $\underset{-d}{\to }$
4. $\underset{b}{\to }$ = $\underset{-d}{\to }$

Q. If $\overrightarrow{a}$ is a vector and $x$ is a non-zero scalar then

1. $x\overrightarrow{a}$ is a vector collinear to $\overrightarrow{a}$
2. $x\overrightarrow{a}$ and $\overrightarrow{a}$ have independent directions
3. $x\overrightarrow{a}$ is a vector in the direction of $\overrightarrow{a}$
4. None of these

Q.
I : If the vectors $\overrightarrow{a}=(1,x,-2)$ , $\overrightarrow{b}=(x,3,-4)$ are mutually perpendicular, then $x=2$
II : If $\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k},\overrightarrow{b}=-\hat{i}+2\hat{j}+\hat{k},\overrightarrow{c}=3\hat{i}+\hat{j}$ and $\overrightarrow{a}+t\overrightarrow{b}$ is perpendicular to $\overrightarrow{c}$ then $t=5$

1. Only I is true
2. Neither l nor ll are true
3. Both I and II are true
4. Only II is true