Question

Write the vector v in terms of i and j whose magnitude and direction angle are given.

||v|| = 5/6, theta = 113 deg

Answer 1

If the magnitude of vector v is ||v|| = 5/6 and the direction angle is θ = 113 degrees, we can use the following formulas to find the components of the vector:

v_x = ||v|| cos θ
v_y = ||v|| sin θ

Plugging in the values, we get:

v_x = (5/6) cos 113° ≈ -0.304
v_y = (5/6) sin 113° ≈ 0.708

Therefore, the vector v can be written in terms of i and j as:

v = v_x i + v_y j
v ≈ -0.304 i + 0.708 j