Question

define dot and cross product of two vectors give two examples of each​

Answer 1

The dot product and cross product are methods of relating two vectors to one another. The dot product is a scalar representation of two vectors, and it is used to find the angle between two vectors in any dimensional space. For vectors and , the dot product is . The cross product is a vector orthogonal to three-dimensional vectors and , and can be used to determine the area or volume of a parallelogram defined by , , and . For vectors and , the cross product is , which is the determinate of a three-by-three matrix. Two vectors are parallel if their cross product is equal to zero, .

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Answer 2

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DOT PRODUCT ☃️

The dot product of two unit vectors is cosine of angle between the vectors. now the magnitude of both is 1 since they are unit vector. So their dot product will be 1 when they are along same direction and if not then their dot product is equal to cosine of the angle between them.

CROSS PRODUCT ☃️

The cross product a × b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span.

READ MORE :-☃️

: a vector c whose length is the product of the lengths of two vectors a and b and the sine of their included angle, whose direction is perpendicular to their plane, and whose direction is that in which a right-handed screw rotated from a toward b along axis c would move.

We know that, cross(vector) product of two vectors is a third vector whose magnitude is given by the product of magnitude of given vectors multiplied by sin ratio of the smaller angle between them. In your case, given two vectors are the same, i.e., A and hence, they are equal in magnitude and angle between them is 0°.

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