Question

A vector is not changed if

• A. it is displaced parallel to itself
• B. it is rotated through an arbitrary angle
• C. it is cross-multiplied by a unit vector
• D. it is multiplied by an arbitrary scalar

Hint:

A vector has both magnitude and direction.

Answer 1

The Correct Option is A

A vector has magnitude and direction. Rotating a vector changes its direction, thus changing the vector itself. Multiplying a vector by a scalar changes its magnitude, but not direction. Displacing a vector parallel to itself does not change the vector.

When a vector is displaced parallel to itself, neither its magnitude nor its direction changes.

Therefore, Option A is the correct answer.

Discover More From Chapter: Motion in a Plane

Answer 2

The Correct Answer is (A)

Real Life Applications

• Reflection: When you gaze in a mirror, your body's image is spread out across the surface of the glass. The reason for this is that the light rays that bounce off of your body also bounce back at the same angle.

• Rotation: A top rotates about its axis when it is spun. The size of the top's velocity vector is constant, but its direction is continually changing.
• Zooming in or out on a map entails a continual scaling of the map. This implies that the same constant is multiplied by the length of each vector on the map.

Question can also be asked as

• Which of the following operations does not change a vector?
• What is the effect of displacing a vector parallel to itself?
• How does rotating a vector through an angle change its magnitude and direction?
• What is the difference between a scalar and a vector?
• What does it mean for a vector to be "changed"?
• What are the properties of a vector that are not changed by certain operations?
• How can we represent the geometric properties of a vector mathematically?

 

 

Answer 3

The Correct Answer is (A)

Vectors represent quantities that have both magnitude and direction. When a vector is displaced along its own direction, its fundamental characteristics remain unchanged. 

• Vectors are often depicted as arrows, with the length representing the magnitude and the orientation indicating the direction.
• Displacement refers to the change in the position of an object or point in space.
• Parallel displacement specifically involves moving an object or point in the same direction without altering its orientation.

Invariance of Vectors

• When a vector is displaced parallel to itself, its properties remain unchanged.
• The magnitude and direction of the vector remain constant throughout the parallel displacement.

Check Out:

Related Concepts
Displacement vector	Resolution of Vectors	Horizontal Motion
Projectile Motion Formula	Trajectory formula	Uniform Circular Motion

 

Mathematical Representation

• Mathematically, if vector A is displaced parallel to itself by a certain distance, resulting in a new position represented by vector B, the two vectors will have the same magnitude and direction.
• Vector A = Vector B in terms of magnitude and direction.

Physical Interpretation

• The invariance of vectors under parallel displacement has important implications in physics.
• It ensures that physical quantities represented by vectors, such as velocity, acceleration, and force, remain consistent regardless of their position in space.

When a vector is displaced along its own direction, its magnitude and direction remain unchanged. This property enables consistent and accurate representations of physical quantities throughout various applications.