# Find the angle between the given vectors - 94893

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## shri21

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• From: Mathematics, Algebra
• Posted on: Wed 20 Jan, 2016
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1. Express V in v1i and v2i form with the given magnitude and direction. Direction = 27° |v| = 2 2. Use DeMoivre's Theorem and leave the answer in a+ bi form. (2-2i)^5 3. Find the indicated roots. Cube roots of -8i 4.Find the quotient and leave the result in a +bi form. 15(cos 240° + i sin 240°) / 3(cos 30° +i sin 30°) 5. Find the angle between the given vectors, to the nearest tenth of a degree. u=5i + 6j, v = 3i -2j 6. Find a*b a = 6i + 9j, b = 4i + 3j
Solution Description

(6) a • b = a1 b1 + a2 b2

= (6 * 4) + (9 * 3) = 24 + 27

= 51

(5) u • v = u1 v1 + u2 v2 = (5 * 3) + (6 * -2) = 3

|u| = √(5^2 + 6^2) = √61 and |v| = √{3^2 + (-2)^2} = √13

Angle between the vectors is given by

cos θ = (u • v)/|u||v|

= 3/(√61 √13)

= 0.1065