Question

Write the vector v in terms of i and j whose magnitude v and direction angle θ are given. v=24, θ=315°?

Answer 1

The vector v with magnitude 24 and direction angle 315° can be expressed in i and j notation as v = 24(√2/2)i - 24(√2/2)j.

Step-by-step explanation:

The vector v written in terms of i and j given its magnitude, v = 24, and direction angle, θ = 315°, can be found using trigonometric functions. The angle of 315° places the vector in the fourth quadrant, where the x-component is positive and the y-component is negative.

Here's how you can write the vector v:

• The x-component (vx) is found using vx = v * cos(θ).
• The y-component (vy) is found using vy = v * sin(θ).

Since the magnitude, v, is 24 and θ is 315°, we have:

• vx = 24 * cos(315°) = 24 * (√2/2)
• vy = 24 * sin(315°) = 24 * (-√2/2)

Therefore, the vector v in i and j notation is:

v = 24(√2/2)i - 24(√2/2)j