The cosine of the angle between two vectors is used in the dot product because it measures the similarity or alignment of the vectors. The dot product calculates the product of the magnitudes of the vectors and the cosine of the angle between them, resulting in a scalar value that represents the degree of alignment or correlation between the vectors.
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
The dot-product of two vectors tells about the angle between them. If the dot-product is positive, then the angle between the two vectors is between 0 and 90 degrees. When the dot-product is negative, the angle is more than 90 degrees. Therefore, the dot-product can be any value (positive, negative, or zero). For example, the dot product of the vectors and is -1*1+1*0+1*0 = -1 which is negative.
Zero.
It depends on what the dot product is meant to be equal to.
The cosine of the angle between two vectors is used in the dot product because it measures the similarity or alignment of the vectors. The dot product calculates the product of the magnitudes of the vectors and the cosine of the angle between them, resulting in a scalar value that represents the degree of alignment or correlation between the vectors.
It depends on the type of product used. A dot or scalar product of two vectors will result in a scalar. A cross or vector product of two vectors will result in a vector.
To multiply two vectors in 3D, you can use the dot product or the cross product. The dot product results in a scalar quantity, while the cross product produces a new vector that is perpendicular to the original two vectors.
The dot-product of two vectors is the product of their magnitudes multiplied by the cosine of the angle between them. The dot-product is a scalar quantity.
The dot-product of two vectors tells about the angle between them. If the dot-product is positive, then the angle between the two vectors is between 0 and 90 degrees. When the dot-product is negative, the angle is more than 90 degrees. Therefore, the dot-product can be any value (positive, negative, or zero). For example, the dot product of the vectors and is -1*1+1*0+1*0 = -1 which is negative.
Zero.
Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.
It depends on what the dot product is meant to be equal to.
zero is the answer
No. The dot product is also called the scalar product and therein lies the clue.
Yes, if the dot product of two nonzero vectors v1 and v2 is nonzero, then this tells us that v1 is PERPENDICULAR to v2. :)
That's the way it is defined.