Every vector in L is some scalar multiple of <2, 1, 2>. The line goes through the origin - the zero multiple of this vector is 0<2, 1, 2> = <0, 0, 0>, a vector that starts and ends at the origin. The line goes through the point (-4, -2, -4), which you can get by taking the -2 multiple of the vector.lypaza said:[PLAIN]http://img62.imageshack.us/img62/5319/49966749.png
What is the scalar multiples of a vector actually?
I was thinking L = c[2 1 2]T
Then I looked for projection of v on L. But I got c in my answers which are not supposed to be...
The scalar product of vectors, also known as the dot product, is a mathematical operation that takes two vectors and produces a single scalar value. It is calculated by multiplying the magnitudes of the vectors and the cosine of the angle between them.
The scalar product has several important properties, including commutativity, distributivity, and associativity. It also follows the law of cosines and the Cauchy-Schwarz inequality.
In physics, the scalar product is used to calculate work and energy, as well as determining the angle between two vectors. It is also used in calculating the magnitude of a vector in a specific direction.
Yes, the scalar product can be negative if the angle between the two vectors is greater than 90 degrees. This indicates that the vectors are pointing in opposite directions.
The geometric interpretation of the scalar product is the projection of one vector onto another. This can be visualized by drawing a right triangle between the two vectors and calculating the length of the adjacent side.