Which of the following is true:
A. Two vectors are said to be identical if their difference is zero.
B. Velocity is not a vector quantity.
C. Projection of one vector on another is not an application of dot product.
D. The maximum space rate of change of the function which is increasing direction of line function is known as gradient of scalar function.
Choose the most appropriate answer from the options given below:
A. Two vectors are said to be identical if their difference is zero.
If and are identical, they have the same magnitude and direction.
Mathematically: .
Verdict: While logically sound, in standard physics terminology, we usually call them Equal Vectors. However, "identical" is often used synonymously. Let's look at the others to find the "most" appropriate technical definition.
B. Velocity is not a vector quantity.
Velocity has both magnitude (speed) and direction.
Verdict: False. Velocity is a fundamental vector quantity.
C. Projection of one vector on another is not an application of dot product.
The projection of on is given by the formula:
Verdict: False. Projection is a primary application of the dot product.
D. The maximum space rate of change of the function which is increasing direction of line function is known as gradient of scalar function.
In vector calculus, the Gradient () of a scalar field is a vector whose magnitude is the maximum rate of change of the function and whose direction is the direction of that maximum increase.
Verdict: True. This is the formal definition of the Gradient.
While Statement A is conceptually okay, Statement D is the most technically accurate and rigorous definition provided in the options.
