# 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. ${120^0}$

Answer

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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.

**Complete step by step answer:**

**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.

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