Question Video: Finding the Cross Product of Vectors of Square | Nagwa Question Video: Finding the Cross Product of Vectors of Square | Nagwa

# Question Video: Finding the Cross Product of Vectors of Square Mathematics

If π΄π΅πΆπ· is a square with a side length of 81 cm, and π is a unit vector perpendicular to its plane, find π¨π© Γ π©π.

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### Video Transcript

If π΄π΅πΆπ· is a square with a side length of 81 centimeters and π is a unit vector perpendicular to its plane, find the cross product of vector π¨π© and vector π©π.

We are told that π΄π΅πΆπ· is a square with a side length of 81 centimeters. We are told that π is a unit vector perpendicular to its plane. And we want to find the cross product of vectors π¨π© and π©π. The cross product of two vectors π¨ and π© is a vector perpendicular to the plane that contains π¨ and π© and whose magnitude is given by the magnitude of vector π¨ multiplied by the magnitude of vector π© multiplied by the magnitude of sin π, where π is the angle between the two vectors.

Since each side of our square has length 81 centimeters, then the magnitude of vector π¨π© is 81. Likewise, the magnitude of vector π©π is 81. Since the vectors are the sides of a square, the angle between them is 90 degrees. The cross product of vectors π¨π© and π©π is therefore equal to 81 multiplied by 81 multiplied by the sin of 90 degrees multiplied by the unit vector π. We know that the sin of 90 degrees is equal to one. 81 multiplied by 81 is 6,561, which means that the cross product of π¨π© and π©π is 6,561π.