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# The cross product of two vectors gives zero when the vectors enclose an angle of A. ${90^0}$B. ${180^0}$C. ${45^0}$D. ${120^0}$

Last updated date: 21st Jul 2024
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Hint: 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.

Cross product: The cross product a$\times$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,
$\overrightarrow a \times \overrightarrow b = a.b.\sin \theta$
Here $\overrightarrow a$ and $\overrightarrow b$ are the two vectors and $\theta$ 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,
$a.b.\sin \theta = 0$
Now as we know that magnitude can’t be zero
So, to make this product zero $\sin \theta$must be zero
So, $\sin \theta = 0$
As $\sin \theta$=0 so the angle must be ${0^0}$ or ${180^0}$.
As given in this question, the option available is ${180^0}$.

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.