Pure Year 2 Unit 12

Question 1

Distance of the origin to the point (x, y, z) =

Answer 1

root(x^2 + y^2 + z^2)

Question 2

Distance between the points (x1, y1, z1) and (x2, y2, z2)

Answer 2

Root((x1 - x2)^2 + (y1 - y2)^2 + (z1 - z2)^2)

Question 3

How are unit vectors on the 3d axes denotes?

Answer 3

I, J, and K for x, y, and z respectively

Question 4

If the vector a = xi + yj + zk makes an angle theta with the positive x axis, how do you find it?

Answer 4

cos(thetax) = x / modulus(a)