Question

Vector A has a magnitude of 5 units lies in the XY- plane and points in a direction 120° from the direction of increasing X. Vector B has a magnitude of 9 units and points along the Z-axis. The magnitude of cross product A x B is
A. 30
B. 35
C. 40
D. 45

Answer 1

Hint: In this question we will use the concept of cross product of a vector quantity. We will find the angle between the two given vector to find out the cross product of the given vectors.

Formula used:
The formula if cross product of two vectors A and B is,
$A×B=|A||B|sinϴ$

Complete step by step solution:
Given, |A|(magnitude of vector A)=5, |B|(magnitude of vector B)=9
Vector A lies in the XY- plane and vector B lies points along the Z-axis. Therefore, the angle between vector A and vector B = 90°.
Cross product of A and B:
$A×B=|A||B|sinϴ$
$\Rightarrow A×B=5\times 9\times sin(90°)$
$\therefore A×B= 45$

The correct answer is D.

Additional Information: The process of multiplying two vectors is called the cross product. The multiplication sign (x) between two vectors indicates a cross product. It has a three-dimensional definition and is a binary vector operation. The third vector that is parallel to the two original vectors is the cross product of the two original vectors. The area of the parallelogram that separates them provides information about its magnitude, and the right-hand thumb rule can be used to identify its direction. Since the outcome of the cross product of vectors is a vector quantity, the cross product of two vectors is also referred to as a vector product. We will discover more about the cross product of two vectors in this article.

Note: In cross product the angle between the two vectors are taken and not between an X,Y or Z axis and the vector. And in cross product sinϴ is used.