Question

Statement-1: The scalar product of two vectors can be zero
Statement-2: If two vectors are perpendicular to each other, their scalar product will be zero.
(A) Both statements 1 & 2 are true. Statement 2 is correct explanation for statement 1
(B) Both statement 1 & 2 are true but Statement 2 is not a correct explanation for statement 1
(C) Statement 1 is true but statement 2 is false.
(D) Statement 1 is false but statement 2 is true.

Answer 1

Hint:Vectors can be multiplied with one other using two product rules- broadly dot product which gives a scalar result and cross-product which gives vector result.

Complete step by step answer:
Suppose we have two vectors \[\overrightarrow{A}\& \overrightarrow{B}\]
Dot product or scalar product of two vectors is given by \[\overrightarrow{A}.\overrightarrow{B}=AB\cos \alpha \]
Where \[\alpha \]is the angle between the two vectors
If both the vectors are not equal to zero then the only way that the dot product of two vectors is equal to zero is making cos\[\alpha \] equal to zero. Let us look at how the value of cos \[\alpha \] varies over the given interval. We know the domain of cos is from -1 to 1. It attains its minimum value, -1 and maximum value, +1. Also, the value of cos \[\alpha \] is equal to zero when \[\alpha \] is equal to \[90{}^\circ \]. And when the value of the angle between the two vectors is \[90{}^\circ \] then the two vectors are said to be perpendicular to each other.
Hence both the statements are true and statement 2 is a correct explanation of statement 1.
Hence the correct option is (A)

Note: While taking either dot product or cross product we have to keep in mind we have to take the angle between the two original vectors.