- #1
brandon2743
- 3
- 0
pretty much this is all i was given.
I have no idea how to even approach it. I do not need an answer (would be nice though), just an idea on how to go about starting it.
HallsofIvy said:Since this is in R3 writing the vector x as <x, y, z>, that dot product will given you a single equation in the three unknowns, x, y, and z. You can solve for one of them in terms of other two. For example, you were to find that z= ax+ by, then you could write your vector as <x, y, z>= <x, y, ax+ by>= x<1, 0, a>+ y<0, 1, b>.
(On the other hand, if you solve for x, say, as x= py+ qz, then you could write the vector as <x, y, z>= <py+ qz, y, z>= y<p, 1, 0>+ z<q, 0, 1>. There are an infinite number of correct solutions to this problem.)
The dot product is a mathematical operation that takes two vectors and produces a scalar value. It is also known as the inner product or scalar product.
The dot product is calculated by taking the sum of the products of the corresponding elements in two vectors. For example, if vector A is [a1, a2, a3] and vector B is [b1, b2, b3], the dot product would be calculated as a1*b1 + a2*b2 + a3*b3.
The dot product has several applications in mathematics and physics. It can be used to calculate the angle between two vectors, determine if two vectors are perpendicular, and calculate the projection of one vector onto another.
Two vectors are perpendicular if their dot product is equal to zero. Geometrically, this means that the two vectors are at a 90 degree angle to each other.
In physics, the dot product is used to calculate the work done by a force on an object. The dot product of the force vector and the displacement vector gives the amount of work done in the direction of the force.