To find the angle between vectors D and E and the x-axis, we can use the dot product formula. By solving the equation, we find that the angle is approximately 142.7°.
To find the angle between two vectors D and E, we can use the dot product formula:
D · E = |D| |E| cos θ
Where |D| and |E| are the magnitudes of the vectors, and θ is the angle between them.
In this case, |D| = √((5i)^2 + (-3j)^2) = √(25 + 9) = √34 and |E| = √((2i)^2 + (j)^2) = √(4 + 1) = √5.
The dot product of D and E can be calculated as D · E = (5i)(2i) + (-3j)(j) = 10i^2 - 3j^2 = 10(-1) - 3(1) = -13.
Substituting the values into the dot product formula: -13 = √34 √5 cos θ.
Next, we can solve for cos θ: cos θ = -13 / (√34 √5).
Taking the inverse cosine of both sides: θ = arccos(-13 / (√34 √5)).
Using a calculator, we find that θ ≈ 142.7°.
Therefore, the angle between vectors D and E and the x-axis is approximately 142.7°.