- What is a scalar?
a) A quantity with only magnitude
b) A quantity with only direction
c) A quantity with both magnitude and direction
d) A quantity without magnitude
2. A unit vector has the magnitude of ___
a) 5
b) 1
c) 10
d) 0
3. Multiplying 2î + 7ĵ by 5 gives ______
a) 10î + 35ĵ
b) 2î + 35ĵ
c) 10î + 7ĵ
d) 2î + 7ĵ
4. The ___________ forces do not cause the rotation.
a) Non-concurrent
b) Concurrent
c) Parallel
d) Non-Parallel
Explanation: The concurrent forces are the which are somewhere touching the axis of rotation. If any of the force is touching that axis, that force is not considered or is insufficient to cause a rotation. If a force is concurrent then the perpendicular distance of the force from the line of an axis is zero, thus no rotation. As we know rotation is caused by a moment.
5. The tendency of a force to rotate the body is called the moment of the force.
a) True
b) False
Explanation: The moment of the force about an axis or a point gives the measure of the tendency of the force. It is the cause of the body’s rotation, about that point or at that axis. Thus, the tendency of a force to rotate the body is called the moment of the force or torque.
6. The moment is the cross product of which two vectors?
a) Force and Radius vectors
b) Radius and Force vectors
c) Force and Radius scalars
d) Radius and Force scalars
Explanation: The cross product needs to take in the proper sequence. If not taken then the answer is just the opposite of the true answer. That’s why, the answer is not the Force and Radius vectors, but the Radius and Force vectors. Because the moment has its direction, as many of the cross products have, and thus precaution needs to be taken.
7. Mass is a ____
a) Scalar quantity
b) Vector quantity
c) Relative quantity
d) Dependent quantity
8. The operation used to obtain a scalar from two vectors is ______
a) Cross product
b) Dot product
c) Simple product
d) Complex product
9. Which of the following statements is false?
a) Cross product is commutative
b) Cross product is distributive over addition
c) Dot product of two vectors gives a scalar
d) Dot product is commutative
10. Find the vector product (a X b) of the two given vectors: a = 2i + 3j + 4k, b = 3i + 5j. Here, i, j & k are unit vectors along three mutually perpendicular axes.
a) -20i + 12j + k
b) 10i + 6j + 1/2k
c) 20i – 12j – k
d) 10i – 6j -1/2k
11. What is the dot product of two vectors which are having a magnitude equal to unity and are making an angle of 45°?
a) 0.707
b) -0.707
c) 1.414
d) -1.414
12. Which of the following is true?
a) i x i =1
b) j x i = -j
c) k x j = -i
d) k x k = 1
13. Which of them is not correct?
a) j x j = 0
b) j x k = i
c) j x i = k
d) j x i = -k
14. What is a scalar?
a) A quantity with only magnitude
b) A quantity with only direction
c) A quantity with both magnitude and direction
d) A quantity without magnitude
15. Which one of the following operations is valid?
a) Vector multiplied by scalar
b) Vector added to scalar
c) Vector subtracted from scalar
d) Vector divided by vector