
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
409.5k+ views
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 $). A vector is the cross product of two vectors.
Complete step by step answer:
Cross product: The cross product a$ \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.
Recently Updated Pages
Master Class 11 Accountancy: Engaging Questions & Answers for Success

Express the following as a fraction and simplify a class 7 maths CBSE

The length and width of a rectangle are in ratio of class 7 maths CBSE

The ratio of the income to the expenditure of a family class 7 maths CBSE

How do you write 025 million in scientific notatio class 7 maths CBSE

How do you convert 295 meters per second to kilometers class 7 maths CBSE

Trending doubts
10 examples of friction in our daily life

One Metric ton is equal to kg A 10000 B 1000 C 100 class 11 physics CBSE

Difference Between Prokaryotic Cells and Eukaryotic Cells

State and prove Bernoullis theorem class 11 physics CBSE

What organs are located on the left side of your body class 11 biology CBSE

Write down 5 differences between Ntype and Ptype s class 11 physics CBSE
