Two vectors and have the components, in meters, ax = 6.91, ay = 1.45, bx = 2.45, by = 7.02. (a) find the angle between the directions of and. there are two vectors in the xy plane that are perpendicular to and have a magnitude of 8.28 m. one, vector, has a positive x component and the other, vector, a negative x component. what are (b) the x component and (c) the y component of, and (d) the x component and (e) the y component of vector?

Question

Amiya Miranda

Mathematics

14 October, 22:54

Two vectors and have the components, in meters, ax = 6.91, ay = 1.45, bx = 2.45, by = 7.02. (a) find the angle between the directions of and. there are two vectors in the xy plane that are perpendicular to and have a magnitude of 8.28 m. one, vector, has a positive x component and the other, vector, a negative x component. what are (b) the x component and (c) the y component of, and (d) the x component and (e) the y component of vector?

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Answers (1)

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Jayson Glenn · Answer 1

We are given

ax = 6.91

ay = 1.45

bx = 2.45

by = 7.02

So,

tan a→ = 1.45/6.91 = 0.2098 = ma

tan b→ = 7.02/2.45 = 2.8653 = mb

To get the angle between the two

tan θ = (mb - ma) / (1 + ma mb)

tan θ = (2.8653 - 0.2098) / (1 + (2.8653) (0.2098))

θ = 58.91°

The x component is

x = 8.28 cos 58.91 = 4.28 m

The y component is

y = 8.28 sin 58.91 = 7.09 m