1. What is the direction of the resultant vector if two vectors having equal length is placed in the Cartesian plane at the origin as, one being parallel to and heading towards positive x-axis and the other making 165 degree with it and heading in the opposite direction of that of the first one?
a) It is either in the 1st quadrant or in the 2nd quadrant
b) It is either in the 1st quadrant or in the 3rd quadrant
c) It is either in the 1st quadrant or in the 4th quadrant
d) Only in the 1st quadrant
Explanation: If one is heading towards positive X-axis and the other is in the other direction opposite to the first one, with both having the same length and having an angle between them being obtuse, means that the direction is to be in the direction of either 1st quadrant or in the 4th quadrant
2. Force vector R is having a______________
a) Length of R and a specific direction
b) Length of R
c) A specific direction
d) Length of magnitude equal to square root of R and a specific direction
Explanation: As it is a force vector, it means it is going to have a direction and a magnitude. The magnitude is not the square root of R, R is just the magnitude of the vector given.
3. The resultant of three equal vectors having mutual angles being 120 degrees and being originated from a single point is zero.
a) True
b) False
Explanation: As one can imagine three vectors coming out of a single point and are having a 120-degree angle with their adjacent ones, the resultant would be zero.
4. Every point on the force vector is having the same magnitude and the same direction as the whole force vector have.
a) True
b) False
Explanation: The vector is made by joining the final and the starting point. If we consider any arbitrary point then the length would be calculated w.r.t the starting point, which might give different magnitude but same direction.
5. In right handed coordinate system which axis is considered to be positive?
a) The thumb is z-axis, fingers curled from x-axis to y-axis
b) The thumb is x-axis, fingers curled from z-axis to y-axis
c) The thumb is y-axis, fingers curled from x-axis to z-axis
d) The thumb is z-axis, fingers curled from y-axis to x-axis
Explanation: As right handed coordinate system means that you are curling your fingers from positive x-axis towards y-axis and the thumb which is projected is pointed to the positive z-axis. Thus visualizing the same and knowing the basic members of the axis will not create many problems.
6. If A is any vector with Ai + Bj + Ck then what is the y-axis component of the vector?
a) B units
b) A units
c) C units
d) Square root of a sum of squares of the three, i.e. A, B and C
Explanation: As the given vector is shown in the Cartesian system, the number with “j” is the Y-axis component of the given vector. With the numbers with “i” representing components of x-axis and “k” representing the z axis respectively.
7. If the force vector F is having its x-axis component being equal to Z N, y-axis component be X N and z-axis component be Y N then vector F is best represented by?
a) Xi + Yj + Zk
b) Yi + Xj + Zk
c) Zi + Yj + Xk
d) Zi + Xj + Yk
Explanation: It is given that x, y and z-axis components are Z, X and Y respectively. Thus, just by placing the right coordinates we get option d to be correct. Here just the interchange of the axis’s representor with their respective axis is creating confusion. Which must be figured out.
8. Which statement is right for force vector F = Ai + Bj + Ck?
a) In rectangular components representation of any vector we have vector F = Ai + Bj + Ck
b) In rectangular components representation of any vector we have vector F = Ax + By + Cz
c) In rectangular components representation of any vector we have vector F = Fx + Fy + Fz
d) In rectangular components representation of any vector we have vector F = Fi + Fj + Fk
Explanation: As given the vector is F = Ai + Bj + Ck, this implies that the x ,y and z-axis components of this vector is A, B and C respectively. But, in rectangular components representation of any vector, the vector is written as F = Fx + Fy + Fz.
9. What is the magnitude of the Cartesian vector having the x, y and z axis components to be A, B and C?
a) Square root of the squares each A, B and C
b) Square of the squares each A, B and C
c) Cube root of the squares each A, B and C
d) Cube of the squares each A, B and C
Explanation: The magnitude of a Cartesian vector having the x, y and z axis components to be A, B and C is always the square root of the squares each A, B and C. This comes from the distance formula between two points in the Cartesian plane. That is the square root of the subtraction of the final and initial point of a line.
10. What is cosα for force vector F = Ax + By +Cz (Given α, β and γ are the angles made by the vector with x, y and z axis respectively)?
a) B/F
b) C/F
c) A/F
d) 1
Explanation: The cosine component of the vector is defined as the ratio of the x-axis component to the magnitude of the vector, i.e. F in this case. Likewise, the sine component is the ratio of the y-axis component to the magnitude of the vector