Sure, to find the angle between two vectors, we can use the formula:

cos θ = (A . B) / (||A|| ||B||)

where:
- A . B is the dot product of A and B
- ||A|| is the magnitude of A
- ||B|| is the magnitude of B

Let's denote A = (i + j + k) and B = (i + j - k).

Step 1: Calculate the dot product (A . B)
A . B = (1*1 + 1*1 + 1*(-1)) = 1

Step 2: Calculate the magnitudes of A and B
||A|| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3)
||B|| = sqrt(1^2 + 1^2 + (-1)^2) = sqrt(3)

Step 3: Substitute these values into the formula
cos θ = 1 / (sqrt(3) * sqrt(3)) = 1/3

Step 4: Find the angle
θ = arccos(1/3)

This is the angle between the two vectors.

Question

Sure, to find the angle between two vectors, we can use the formula:

cos θ = (A . B) / (||A|| ||B||)

where:
- A . B is the dot product of A and B
- ||A|| is the magnitude of A
- ||B|| is the magnitude of B

Let's denote A = (i + j + k) and B = (i + j - k).

Step 1: Calculate the dot product (A . B)
A . B = (1*1 + 1*1 + 1*(-1)) = 1

Step 2: Calculate the magnitudes of A and B
||A|| = sqrt(1^2 + 1^2 + 1^2) = sqrt(3)
||B|| = sqrt(1^2 + 1^2 + (-1)^2) = sqrt(3)

Step 3: Substitute these values into the formula
cos θ = 1 / (sqrt(3) * sqrt(3)) = 1/3

Step 4: Find the angle
θ = arccos(1/3)

This is the angle between the two vectors.

Knowee AI · Accepted Answer