Chapter 12 Vectors (Year 2)

Question 1

What is the formula for the distance from the origin to the point (x, y, z)?

Answer 1

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

Question 2

What is the formula for the distance from the point (x1, y1, z1) to the point (x2, y2, z2)?

Answer 2

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

Question 3

What is pi + qj + rk equivalent to?

Answer 3

Unit vector: (p q r)

Question 4

If the vector a (xi + yj + zk) makes an angle theta_x with the positive x-axis what is cos theta_x?

Answer 4

Cos theta_x = x/|a|

Question 5

If pi + qj + rk = ui + vj + wk what does p, q and r equal?

Answer 5

• p = u
• q = v
• r = w