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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{90^0}
B. 1800{180^0}
C. 450{45^0}
D. 1200{120^0}

Explanation

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×\timesb 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\overrightarrow a \times \overrightarrow b = a.b.\sin \theta
Here a\overrightarrow a and b\overrightarrow b are the two vectors and θ\theta is the angle between two vectors. Here aa and bb are the magnitudes of both vectors

As given in the question, the cross product is zero. Therefore,
a.b.sinθ=0a.b.\sin \theta = 0
Now as we know that magnitude can’t be zero
So, to make this product zero sinθ\sin \theta must be zero
So, sinθ=0\sin \theta = 0
As sinθ\sin \theta =0 so the angle must be 00{0^0} or 1800{180^0}.
As given in this question, the option available is 1800{180^0}.

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 (×\times). A vector is the cross product of two vectors.