3D Vectors Cross and Dot Products?

Question

a = 4i + 3j
b = 2i - j
c = 2i + j + 3 k
d = 2i - 2j + k

Questions:
(1) c x (a.b)
(2) (c x s) + (d x c)

edit

(2) (c x d) + (d x c)

Answer 1

(1) (a.b) is a scalar, but x works on two vectors, so this operation doesn't make sense, as written. If you actually mean multiplying the vector c by the scalar (a.b), then: a.b=8-3=5, so c(a.b) = 10i+5j+15k.
(2) d x c = (2,-2,1) x (2,1,3) = (-7,-4,6), or -7i - 4j + 6k.

c x d = -(d x c), so the sum is the zero vector, 0i + 0j + 0k.

Answer 2

Dot product is a scalar this is defined via it is formula (the only you do not prefer me to print). Intuitively we would bear in mind a vector D and a unit vector u then the 'element' of D alongside the direction u is given via D.U. this is as intuitive because it gets i'm afraid. If D is a displacement vector then it varieties a real triangle with base (adjacent) length D.U alongside u. go product is a vector this is derived from the thought 2 vector (say D and u as quickly as extra) describe a plane, the plane in turn defines purely one potential vector perpendicular to the 1st 2 in a desirable exceeded sense. We then define the bypass product to be this vector. Intuitively we would opt to take the magnitude of the bypass product to be the dimensions of the 'opposite' element of our desirable triangle (from till now than). In thought it could have any magnitude we want in spite of if by way of fact we've already have been given the adjacent length of the triangle from D.U we would exceptionally much as good define Dxu this form for completeness. it is obvious then that Dxu includes a similar understand-how as D.U (in that the suggestions-set between the vectors will additionally be got here across) in spite of if it additionally includes added wisdom approximately D and u: it tells us that they exist in a terrific defined plane, one we can to find if all of us understand Dxu. D.U simplest tells us the perspective between the vectors without giving something away with reference to the plane they each and every lie in.

Answer 3

What in tarnation?