Question
Question: The cross product of two vectors gives zero when the vectors enclose an angle of A. \({90^0}\) ...
The cross product of two vectors gives zero when the vectors enclose an angle of
A. 900
B. 1800
C. 450
D. 1200
Solution
To answer this question, we first need to understand what is a vector. A vector is a two-dimensional object with both magnitude and direction. A vector can be visualized geometrically as a guided line segment with an arrow indicating the direction and a length equal to the magnitude of the vector.
Complete step by step answer:
Cross product: The cross product a×b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a magnitude equal to the area of the parallelogram that the vectors span and a direction given by the right-hand law.Cross product formula of two vectors,
a×b=a.b.sinθ
Here a and b are the two vectors and θ is the angle between two vectors. Here a and b are the magnitudes of both vectors
As given in the question, the cross product is zero. Therefore,
a.b.sinθ=0
Now as we know that magnitude can’t be zero
So, to make this product zero sinθmust be zero
So, sinθ=0
As sinθ=0 so the angle must be 00 or 1800.
As given in this question, the option available is 1800.
Hence, the correct answer is option B.
Note: In three-dimensional spaces, the cross product, area product, or vector product of two vectors is a binary operation on two vectors. It is denoted by the symbol (×). A vector is the cross product of two vectors.