Question

Question 1. Determine whether the vectors u and v are parallel, orthogonal, or neither. u = <10, 6>, v = <9, 5>? Question 2. Find the angle between the given vectors to the nearest tenth of a degree.
u = <6, -1>, v = <7, -4>

20.3°/ 10.2°/ 0.2°/ 30.3° Question 3. Express the complex number in trigonometric form. -6i 6(cos 0° + i sin 0°) 6(cos 270° + i sin 270°) 6(cos 180° + i sin 180°) 6(cos 90° + i sin 90°)

Answer 1

Angle between two vectors = arc cos [(u.v)/(abs(u) x abs (v))]
u.v = (10 x 9) + (6 x 5) = 90 + 30 = 120
abs (u) = $\sqrt{ 10^{2}+ 6^{2}} = \sqrt{100+36} = \sqrt{136} =11.66$
abs (v) = $\sqrt{ 9^{2}+ 5^{2}} = \sqrt{81+25} = \sqrt{106} =10.30$
Angle between the two vectors = arc cos [120 / (11.66 x 10.30)] = arc cos [120 / 120.1] = arc cos [1] = 0
Since the angle between the two vectors is 0,
therefore, the angles are parallel