Question 1: Choose the correct answer
1- What will be the cross product of the vectors 2i + 3j + k and 6i + 9j + 3k?
- a) i + 2j + k
- b) i - j - 5k
- c) 0
- d) 2i - j - 5k
Explanation: The second vector is exactly 3 times the first vector (6i + 9j + 3k = 3 × (2i + 3j + k)). Because they are parallel, their cross product is 0.
2- A vector of magnitude √2 units along the internal bisector of the angle between the vectors 2i - 2j + k and i + 2j + 2k:
- a) j + k
- b) i - j
- c) i - k
- d) i + k
3- Which of the following equals a x b (where a and b are two vectors)?
- a) -(a x b)
- b) a.b
- c) b x a
- d) -(b x a)
4- What is the magnitude of resultant of cross product of two parallel vectors a and b?
- a) |a|.|b|
- b) |a|.|b| cos(180)
- c) |a|.|b| sin(180)
- d) 1
5- In a coordinate system, a vector is oriented at an angle θ with respect to the x-axis. The y-component of the vector equals the vector's magnitude multiplied by which trigonometric function?
- a) Sin θ
- b) Cot θ
- c) Cos θ
- d) Tan θ
6- A passenger on a bus moving east sees a man standing on a curb. From the passenger's perspective, the man appears to:
- a) Move west at a speed that is equal to the bus's speed
- b) Move west at a speed that is less to the bus's speed
- c) Standstill
- d) Move east at a speed that is equal to the bus's speed
7- Which one of the following statements is true?
- a) A scalar quantity is the one that is conserved in process
- b) A scalar quantity is one that can never take a negative values
- c) A scalar quantity has the same value for the observers with different orientation of axis
- d) More than one of the above