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.
a vector is a line with direction and distance. there is no answer to your question. the dot is the angular relationship between two vectors.
(i) They are linearly dependent since the 2nd vector is twice the 1st vector. All 3 vectors lie in the x-z plane, so they don't span 3D space. (ii) They are linearly independent. Note that the cross-product of the first two is (-1,1,1). If the third vector is not perpendicular to the above cross-product, then the third vector does not lie in the plane defined by the first two vectors. (-1,1,1) "dot" (1,1,-1) = -1+1-1 = -1, not zero, so 3rd vector is not perpendicular to the cross product of the other two.
At the lower levels it stands for multiplication, at more advanced levels it stands for the cross product of vector multiplication (in three or seven dimensions). The multiplication operator can also be a dot on the line ( . ), a dot above the line ( 𝆴 ), an asterisk ( * ), and probably some other symbols as well.
Because in dot product we take projection fashion and that is why we used cos and similar in cross product we used sin
Multiply the product of their magnitudes by the cosine of the angle between them.
We use the dot product cos and in vector we use the vector product sin because of the trigonometric triangle.
The magnitude of dot product of two vectors is equal to the product of first vector to the component of second vector in the direction of first. for ex.- A.B=ABcos@
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.
arithmetic mean
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.
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.
Yes and no. It's the dot product, but not the cross product.
a vector is a line with direction and distance. there is no answer to your question. the dot is the angular relationship between two vectors.
Unit vectors are perpendicular. Their dot product is zero. That means that no unit vector has any component that is parallel to another unit vector.
Your question makes no sense I'm afraid. However the vector product that produces a scalar is the 'dot product'
The product of scalar and vector quantity is scalar.
here are the possible answers: A) A tridimensional vector B) A 4D vector C) A 5D vector D) An scalar number E) It is undefined