Definition of Vector

Q. Two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ are such that $|\overrightarrow{a}|=8\text{units},$ angle between both vectors is ${60}^{\circ }.$ Then the projection(in $\text{units}$) of $\overrightarrow{a}$ along $\overrightarrow{b}$ is equal to

Q.

Consider points $A,B,C$ and $D$ with position vectors $(6,-4,7),(1,-6,10),(-1,-3,4)\text{and}(5,-1,5)$ respectively. Then quad $ABCD$ will have

1. three sides equal
2. two sides equal
3. all the sides unequal
4. four sides equal

Q.

Which of the following quantities are vectors.

1. 70 cm³
2. 5 m/s
3. 8m/s NE
4. 70 cm to the right
5. ${25}^{\circ }C$
6. 30N (force)

1. 3, 4
2. None of them
3. All of them
4. 1, 2, 5 and 6

Q.

I throw a ball with some force. The linear distance the ball covers is 30m. This physical quantity, distance of 30m is a vector quantity.

1. True

2. False

Q. The magnitude of the position vector of the point (3, 4) will be ___

Q. A vector $\overrightarrow{a}$ has components 2p and 1 with respect to a rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to the new system. $\overrightarrow{a}$ has components p + 1 and 1, then

1. $p=1orp=-1$
2. $p=1orp=-\frac{1}{3}$
3. $p=-1orp=\frac{1}{3}$
4. p = 0

Q. Which of the following quantities are vectors

1. 70 m
2. 80 kg
3. 6 km North
4. 80 N downwards
5. 78 m/s to left
6. 55 seconds
7. 30 °C
8. 5 N/C
9. 3 Tesla

Q. Find a vector in the direction of vector which has magnitude 8 units.

Q. Classify the following as scalar and vector quantities. (i) time period (ii) distance (iii) force (iv) velocity (v) work done

Q. Classify the following measures as scalars and vectors. (i) 10 kg (ii) 2 metres north-west (iii) 40° (iv) 40 watt (v) 10 –19 coulomb (vi) 20 m/s 2