How to find the angle between two 3-dimensional vectors:
The formula to find the cosine of the angle is: cosA= u.v/|u|x|v|; 1.u.v means that you multiply the x coordinates together, then the y coordinates and the z coordinates, and add them all together: (x1x2+y1y2+z1z2); 2.|u|x|v| means that you have to find the distance from the origin forboth coordinates and times them together: √(x12+y12+z12)√(x22+y22+z22). 3. This means that if vector u is (2,3,4) and vector v is (5,6,7), the cosine of the angle between them willbe:cosA=(2x5+3x6+4x7)/√(22+32+42)x√(52+62+72) = (10+18+28)/√(4+9+16)x√(25+36+49)=56/√29x√110=0.9915; and therefore A= cos-10.9915= 7.47579˚≈ to 3 s.f.
FF
Related Maths A Level answers
All answers ▸When I try to integrate by parts, I end up in an infinite loop. Why is this, and how do you stop?
A curve has parametric equations x= 2sin(t) , y= cos(2t) + 2sin(t) for -1/2 π≤t≤ 1/2π , show that dy/dx = - 2sin(t)+ 1
Integral of sin^x dx
The arithmetic series is given by (k+1)+(2k+3)+(3k+5)+...+303. a)Find the number of term in the series in terms of k. b) Show that the sum of the series is given by (152k+46208)/(k+2). c)Given that S=2568, find k.