To find the angle between the vectors i + 5j and 5i - j, we can use the dot product formula:
a · b = |a||b| cos θ
where a and b are the two vectors, |a| and |b| are their magnitudes, and θ is the angle between them.
First, we need to find the dot product of the two vectors:
(i + 5j) · (5i - j) = (1)(5) + (5)(-1) = 0
Next, we need to find the magnitudes of the two vectors:
| i + 5j | = √(1² + 5²) = √26
| 5i - j | = √(5² + (-1)²) = √26
Now we can substitute the dot product and magnitudes into the dot product formula to solve for θ:
0 = (√26)(√26) cos θ
cos θ = 0
θ = 90°
Therefore, the angle between i + 5j and 5i - j is 90 degrees. Option (D) is the correct answer.