Practice Questions on Cross Product
Q1: Given two vectors ( [Tex]\vec{A} [/Tex]= ❬ 1, 2, -3 ❭) and ( [Tex]\vec{B}[/Tex] = ❬ 2, -1, 4 ❭ ), find ( [Tex]\vec{A} \times \vec{B} [/Tex]).
Q2: Find the area of the parallelogram formed by the vectors ( [Tex]\vec{A}[/Tex] = ❬ 3, -2, 1 ❭) and ( [Tex]\vec{B}[/Tex] = ❬ 1, 4, -2 ❭).
Q3: If ( [Tex]\vec{A} \times \vec{B}[/Tex] = ❬ 2, -3, 5 ❭), and ( |[Tex]\vec{A}[/Tex]| = 4 ) and ( |[Tex]\vec{B}[/Tex]| = 3 ), find the angle between ( [Tex]\vec{A}[/Tex] ) and ( [Tex]\vec{B}[/Tex] ).
Q4: Determine the cross product of the vectors ( [Tex]\vec{A} [/Tex]= ❬ -2, 5, 1 ❭) and ( [Tex]\vec{B}[/Tex] = ❬ 3, -1, 2 ❭).
Q5: Given that the cross product of two vectors ( [Tex]\vec{A} \times \vec{B}[/Tex] ) yields ( [Tex]\vec{C}[/Tex] = ❬ 4, -3, 2 ❭), and ( |[Tex]\vec{A}[/Tex]| = 2 ) and ( |[Tex]\vec{B}[/Tex]| = 3 ), find the magnitude of ( [Tex]\vec{C}[/Tex] ).
Cross Product
Cross product or vector product is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space. Cross product, also called the vector cross product, is a mathematical operation performed on two vectors in three-dimensional space.
In this article, we will understand the meaning of cross product, its definition, the formula of the cross product, the cross product of perpendicular vectors, the cross product of parallel vectors, the right-hand rule cross product and the properties of the cross product.
Table of Content
- What is Cross Product?
- Formula of Cross Product
- Cross Product of Perpendicular Vectors
- Cross Product of Parallel Vectors
- Right-Hand Rule Cross Product
- Matrix Representation of Cross Product
- Triple Cross Product
- Cross Product Properties
- Application of Cross Product