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What is the angle between the given vector and the positive direction of the x-axis?

$ 8i + 6j $

$$\approx 36.87^{\circ}$$

01:07

Alan G.

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

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for the following problem, we want to find the angle between the given vector and the positive direction of the X. Axis. So our vector in this case is going to be eight I Plus six J. So in component form it can be 86. We want to remember the data. The angle that the vector creates is going to be the inverse tangent of E over A. Where B. Is the Y component of the vector and A. Is the X. Component of the vector. So we're gonna copy this down here, we're going to let be equal six and A equals eight. So this is gonna be the inverse tangent of 3/4 which is gonna end up giving us 36 .869 897°. So we can round this off to about 3687°. Um And that will be our final answer.

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