The positions of points A and B are given by the vectors?

Question

a = [17,-18,-16]
and
b=[13,-8,-9]

(i) Find the vector AB
What is its magnitude?

(ii) Determine the angle, in degrees, between 0 and 180, that AB makes with the x axis.

(iii) Determine the angle, in degrees, between 0 and 180, that AB makes with the y axis.
(iv) Determine the angle, in degrees, between 0 and 180, that AB makes with the z axis.

Answer 1

I can help with part a!

Vector AB is -4, 10, 7

magnitude is: square root of ( (-4) squared + (10) squared + (7) squared

so thats is square root of (16+ 100 + 49)
So square root of 165

Answer 2

You need to create a unit vector.

The actual vector is (find the differences : final - initial)

-4i +10j + 7k

The magnitude is the sq. root of the sum of the squares.

(16 + 100 + 49)^0.5 = 12.85

The unit vector is the actual vector divided by the unit vector.

-0.311i + 0.778j + 0.545k
NOTE: The magnitude of the unit vector is 1

The angles are then the inverse cos of the unit values

108.14 degrees x
38.88 degrees y
56.98 degrees z

Answer 3

1) Vector AB = b - a = (-4,10,7)
Magnitude = (16+100+49)^(1/2) = 12.8

Angles are:-
X axis
arc(cos) (-4/12.8) =108.2°
Y axis
arc(cos)(10/12.8) = 38.6°
Z axis
arc(cos)(7/12.8) = 56.8°

Many years since I last did this so hope memory isn`t failing me!