Vectors And Equilibrium MCQs
A vector F of magnitude 20 N makes an angle of 30° with the x-axis. Its x-component is:
The process of splitting a vector into its perpendicular components is called:
Vector Addition
Resolution of a vector
Scalar Multiplication
Resultant vector
Given A = 2i + 5j and B = 3i - 2j. The y-component of the resultant vector R = A + B is:
A vector has components Ax = -8 units and Ay = -6 units. What is the magnitude of the vector?
14 units
10 units
2 units
50 units
If three forces F1, F2, and F3 are in equilibrium, then:
F1 + F2 = F3
F1 x F2 = F3
F1 + F2 + F3 = 0
The x-components are positive, but y-components are negative.
The direction of a vector in a plane is given by θ = tan⁻¹(Ay/Ax). If both Ax and Ay are negative, the vector lies in the:
1st quadrant
2nd quadrant
3rd quadrant
4th quadrant
A boat is moving with velocity Vb = 4i + 3j m/s and the river flows with velocity Vr = -2i - 1j m/s. What is the resultant velocity of the boat?
2i + 2j m/s
6i + 4j m/s
2i + 4j m/s
-8i - 3j m/s
If a vector is multiplied by a negative scalar (e.g., -2), its direction:
Remains unchanged
Becomes perpendicular
Reverses
Is halved
For the addition of vectors by rectangular components, the vectors must first be:
Placed tail to tail
Made parallel to each other
Resolved into their respective components
Scaled to have the same magnitude
What is the magnitude of the resultant of two forces, 3 N and 4 N, acting at a right angle to each other?
The effective value of a vector in a particular direction is called its:
Magnitude
Unit vector
Component
Null vector
To find the direction of a resultant vector R, which formula is used?
θ = sin⁻¹(Ry/Rx)
θ = cos⁻¹(Rx/Ry)
θ = tan⁻¹(Ry/Rx)
θ = tan⁻¹(Rx/Ry)
A vector A lies on the negative y-axis. Its x-component is:
Equal to its magnitude
Negative
Positive
Zero
If Rx = 10 and Ry = -10, the angle θ with respect to the positive x-axis is:
The scalar product of two vectors A and B is denoted by:
If |A| = 5, |B| = 4, and the angle between them is 60°, then A · B is:
The scalar product of two anti-parallel vectors (angle 180°) is:
Maximum positive
Maximum negative
Zero
Equal to the cross product
What is the value of i · j?
What is the value of k · k?
The scalar product is defined as the product of the magnitude of one vector and the component of the second vector __________ to the first.
Perpendicular
Parallel
Opposite
Equal
Which of the following is a scalar quantity?
If A · B = -AB, the vectors are:
Parallel
Perpendicular
Anti-parallel
The statement is impossible
The scalar product is also known as the:
Cross product
Vector product
Dot product
Outer product
For vectors A = 3i and B = 4j, what is A · B?
If two vectors have the same direction, their scalar product is simply the:
Sum of their magnitudes
Difference of their magnitudes
Product of their magnitudes
Ratio of their magnitudes
The property A · B = B · A is known as the:
Associative law
Distributive law
Commutative law
Anti-commutative law
The projection of vector B onto vector A is given by:
The result of a vector product of two vectors is always a:
Scalar
Vector
Number
Unit vector
The magnitude of the vector product is maximum when the angle between the vectors is:
What is the value of i x i?
What is the value of i x j?
The vector product is also known as the:
Dot product
Scalar product
Inner product
Cross product
The property A x B = -B x A shows that the vector product is:
Commutative
Anti-commutative
Associative
Distributive
If |A| = 2, |B| = 3, and the angle between them is 30°, then the magnitude of A x B is:
The direction of torque, defined as τ = r x F, is found using the:
Left-hand rule
Head-to-tail rule
Right-hand rule
Pythagorean theorem
The magnitude of the vector product |A x B| represents the:
Volume of a cube
Area of the parallelogram formed by A and B
Length of the diagonal of the parallelogram
Perimeter of the parallelogram
If two vectors are parallel, their vector product is:
A unit vector
A null vector
Maximum
A scalar quantity
Which of the following is an example of a vector product?
Angular momentum
Kinetic energy
Power
Electric potential
If A points North and B points West, the direction of A x B is:
Up (out of the page)
Down (into the page)
East
South
The vector product is used to define:
Work
Torque
Potential Energy
Mass
A physical quantity that requires both magnitude and direction for its complete description is called a:
Scalar
Vector
Tensor
Dimension
In the graphical representation of a vector, its magnitude is represented by the:
Arrow head
Starting point (tail)
Angle with the x-axis
Length of the arrow
The starting point of a vector is called its:
A vector with zero magnitude and an arbitrary direction is known as a:
Unit vector
Position vector
Null vector
Resultant vector
A dimensionless vector with a magnitude of 1, used only to represent direction, is called a:
Null vector
Unit vector
Free vector
Position vector
How is the unit vector  obtained from vector A?
By multiplying the vector by its magnitude
By dividing the vector by its magnitude
By taking the square of the vector
By finding its components
The unit vector along the y-axis in a Cartesian coordinate system is represented by:
The subtraction of vector B from vector A is equivalent to:
Adding A and B
The dot product of A and B
The cross product of A and B
Adding negative vector B to vector A
The 'head to tail rule' is a graphical method for:
Finding the components of a vector
Multiplying two vectors
Adding two or more vectors
Finding the angle between two vectors
The turning effect produced in a body about a fixed point by a force is known as:
Momentum
Torque
Equilibrium
Inertia
Torque is a vector quantity defined by the vector product:
τ = F x r
τ = r x F
τ = F · r
τ = m a
At what angle between the position vector r and force F is the torque at its minimum (zero) value?
The perpendicular distance from the axis of rotation to the line of action of the force is called the:
Position vector
Moment arm
Equilibrant
Pivot
Two parallel forces of equal magnitude but opposite direction separated by a distance 'd' form a:
Torque
Couple
Concurrent force system
Null vector
If you push on a door handle at an angle of 90° to the door, the torque you produce is:
Minimum
Maximum
Negative
Zero
The study of objects in equilibrium is called:
Dynamics
Kinematics
Statics
Thermodynamics
What is the First Condition of Equilibrium?
The vector sum of all torques is zero.
The vector sum of all forces is zero.
The acceleration of the body is constant.
The angular velocity is zero.
What is the Second Condition of Equilibrium?
The vector sum of all torques is zero.
The vector sum of all forces is zero.
The velocity of the body is constant.
The linear momentum is conserved.
A paratrooper falling with a constant velocity is an example of:
Static equilibrium
Dynamic translational equilibrium
Dynamic rotational equilibrium
Unstable equilibrium
A book resting on a table is in:
Static equilibrium
Dynamic equilibrium
Rotational motion
A non-inertial frame
Forces whose lines of action pass through a common point are called:
Parallel forces
Concurrent forces
Non-concurrent forces
Coplanar forces
The first condition of equilibrium (ΣF = 0) ensures that there is no:
Rotational acceleration
Translational acceleration
Constant velocity
Change in direction
For a body to be in *complete* equilibrium, which condition must be met?
Only the first condition is satisfied.
Only the second condition is satisfied.
Both the first and second conditions must be satisfied.
The net force must equal the net torque.
The single force that can balance a system of concurrent forces is called the:
Resultant force
Net force
Equilibrant force
Normal force
By convention, anti-clockwise torques are taken as ________, and clockwise torques as ________.
Positive, Positive
Negative, Positive
Positive, Negative
Negative, Negative
Other Physics Topics MCQs
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