Let A = (0, 1, 5) ,B = . Find the angle between A and B.
To find the angle between vectors A and B, you can use the dot product formula:
A · B = ||A|| ||B|| cos(theta)
Where A · B is the dot product of vectors A and B, ||A|| and ||B|| are the magnitudes of vectors A and B, respectively, and theta is the angle between the vectors.
Let's calculate the required values:
A = (0, 1, 5)
B = (?)
You didn't provide the coordinates for vector B, so we cannot calculate the dot product, magnitudes, or the angle between A and B without knowing the values of B. Please provide the coordinates for vector B, and we will be able to help you further.
To find the angle between two vectors A and B, we can use the dot product formula and the magnitude formula.
Step 1: Calculate the dot product of A and B:
A · B = (A_x * B_x) + (A_y * B_y) + (A_z * B_z)
Given that A = (0, 1, 5) and B =
A · B = (0 * ) + (1 * ) + (5 * )
Step 2: Calculate the magnitudes of A and B:
||A|| = √(A_x^2 + A_y^2 + A_z^2)
||B|| = √(B_x^2 + B_y^2 + B_z^2)
||A|| = √(0^2 + 1^2 + 5^2)
||B|| = √( ^2 + ^2 + ^2)
Step 3: Calculate the angle between A and B:
cosθ = (A · B) / (||A|| * ||B||)
Step 4: Find the angle θ using the inverse cosine function:
θ = cos^(-1)(cosθ)
Now, let's plug in the values and calculate the angle. Please provide the values of B_x, B_y, B_z.