I don't like your use of ^ in this context.
^ is usually used to show exponents
r1 = (2i+3j+2k) + m(5i-4j+3k)
r1 = (2 + 5m , 3 - 4m , 2 + 3m)
in the same way
r2 = (5 +u , 5 - 3u , -1 + 3u)
at their intersection:
2+5m = 5+u and 3-4m = 5-3u
5m - 3 = u and 3u = 2 + 4m
sub the first into the second
3(5m-3) = 2 + 4m
15m - 4m = 2 + 9
m = 1
u = 2
check for the 3rd component, that is, is 2+3m = -1 + 3u ?
LS = 2+3m = 2+3=5
RS = -1 + 3u = -1 +6 = 5
yes, they intersect
b) at what point?
r1 = (2,3,2) + 1(5,-4,3) = (7,-1, 5)
so the position vector to reach that point is
r = 7i - j + 5k
c)the direction vector of the first line is (5,-4,3)
and of the second line is (1,-3,3)
let Ø be the angle between them, you should know the definition of the dot product .....
(5,-4,3)•(1,-3,3) = |(5,-4,3)| |(1,-3,3)| cosØ
5 + 12 + 9 = √50√19 cos Ø
cos Ø = 26/√950 = .....
I got Ø = appr. 32.5° or .567 radians
Answer this Question
Physics - What are the products (either vector or scalar for each answer) of: a...
Math - Multiplying a vector by a scalar results in: a) a scalar b) a ...
Vactors 12 - Let A and B be any two points on the plane and O be the origin. ...
Vectors - Use a specific example to explore how the cross product behaves under ...
Physics - Displacement is which of the following types of quantities? A. vector ...
Physics - please check these: which of the following is an example of a vector ...
maths - Using properties of the triple scalar product and triple vector product...
physics - A force vector has a magnitude of 576 newtons and points at an angle ...
Maths - Properties of Planes - write a scalar equation, given it's vector ...
math - How do you solve system of equations and tell if they're consistant and ...