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.
If by "triple dot product" you mean u·v·w, then no, because that would imply the existence of a dot product between a vector and a scalar.
cross: torque dot: work
No. The dot product is also called the scalar product and therein lies the clue.
We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
It depends on what the dot product is meant to be equal to.
They are the same.
A dot product is a scalar product so it is a single number with only one component. A cross product or vector product is a vector which has three components like the original vectors.
A Dot product is a very useful tool in both mechanics and 3D graphics. It calculates the cosine of the angle between two vectors.In two-dimensional space, the dot product of vectors [a, b] and [c, d] is ac + bd.Mechanical work is the dot product of force and displacement vectors.Magnetic flux is the dot product of the magnetic field and the area vectors.
Because in dot product we take projection fashion and that is why we used cos and similar in cross product we used sin
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.
Vectors are said to be orthogonal if their dot product is zero.Vectors in Rn are perpendicular if they are nonzero and orthogonal.