
When two vectors are perpendicular their cross product is zero?
Answer
435.6k+ views
Hint: First, we define the terms vector, cross product, and perpendicular and solve the given problem further.
Vector has the magnitude and direction, where magnitude is also known as the size.
The length of the line or arrow shows the magnitude and arrowhead points ( ) is the direction.
Cross product vectors are the two vectors that can be defined as a binary operation on two vectors in three-dimensional spaces.
The cross-vector product of the vector always equals the vector.
Perpendicular is the line and that will make the angle of with one another line.
Complete step by step answer:
First, given that the two vectors are perpendicular to each other, we can say if the two vectors are perpendicular to each other then the vectors angle between them will be equals to the
The cross product of the given each vector equals the product of their magnitudes and sine of the angle between them
The magnitudes of the vectors are written as in the form of
Given that two vectors are perpendicular then we get
Substitute the value of sine in the magnitudes of the vector, we get
Since as from the trigonometric formula, (since the first quadrant touches the circumference of any circle with the y-axis and becomes a fraction of )
Thus, we get,
Therefore, when two given vectors are perpendicular then their cross product is not zero but the dot product is zero.
Note: The commutative property holds in the scalar , and not hold in the vector products as
Parallel lines will not intersect with any of the other lines, unlike the perpendicular lines.
Parallel lines are more likely the straight lines in the given plane.
Since but and
Also
Vector has the magnitude and direction, where magnitude is also known as the size.
The length of the line or arrow shows the magnitude and arrowhead points (
Cross product vectors are the two vectors that can be defined as a binary operation on two vectors in three-dimensional spaces.
The cross-vector product of the vector always equals the vector.
Perpendicular is the line and that will make the angle of
Complete step by step answer:
First, given that the two vectors are perpendicular to each other, we can say if the two vectors are perpendicular to each other then the vectors angle between them will be equals to the
The cross product of the given each vector equals the product of their magnitudes and sine of the angle between them
The magnitudes of the vectors are written as in the form of
Given that two vectors are perpendicular then we get
Substitute the value of sine in the magnitudes of the vector, we get
Since as from the trigonometric formula,
Thus, we get,
Therefore, when two given vectors are perpendicular then their cross product is not zero but the dot product is zero.
Note: The commutative property holds in the scalar
Parallel lines will not intersect with any of the other lines, unlike the perpendicular lines.
Parallel lines are more likely the straight lines in the given plane.
Since
Also
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