Find the angle between the vectors A=6i+8j+10k
B=6i+8j-10k
use dot product
|A| |B| cos theta = A dot B
= 36+64 -100 = 0
LOL, cos theta = 0
so theta = 90 degrees
Helpful
To find the angle between two vectors A and B, we can use the dot product formula:
A ⋅ B = |A| |B| cos(θ)
Where A ⋅ B represents the dot product of vectors A and B, |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between the vectors.
Let's calculate the dot product of vectors A and B:
A ⋅ B = (6 * 6) + (8 * 8) + (10 * -10)
= 36 + 64 - 100
= 0
Next, let's calculate the magnitudes of vectors A and B:
|A| = √(6^2 + 8^2 + 10^2)
= √(36 + 64 + 100)
= √200
= 10√2
|B| = √(6^2 + 8^2 + (-10)^2)
= √(36 + 64 + 100)
= √200
= 10√2
Substituting the values into the dot product formula:
0 = (10√2) (10√2) cos(θ)
Simplifying:
0 = 200 cos(θ)
To find the angle θ, we need to solve for cos(θ). Since the cosine of θ is zero, it means that θ is 90 degrees or π/2 radians.
Therefore, the angle between vectors A and B is 90 degrees or π/2 radians.
To find the angle between two vectors, you can use the dot product formula:
A • B = |A| * |B| * cos(θ)
Here, A • B represents the dot product of vectors A and B, |A| and |B| represent the magnitudes of vectors A and B respectively, and θ represents the angle between them.
Let's calculate the dot product of A and B:
A • B = (6 * 6) + (8 * 8) + (10 * -10)
= 36 + 64 - 100
= 0
Next, calculate the magnitudes of vectors A and B:
|A| = √(6^2 + 8^2 + 10^2)
= √(36 + 64 + 100)
= √200
= 10√2
|B| = √(6^2 + 8^2 + (-10)^2)
= √(36 + 64 + 100)
= √200
= 10√2
Now we have the dot product and the magnitudes, we can substitute them into the dot product formula to find the angle:
0 = (10√2) * (10√2) * cos(θ)
To solve for cos(θ), let's simplify the equation:
0 = 200 * cos(θ)
Since the left side is zero, we can conclude that cos(θ) = 0. To find the values of θ, we need to find the angles θ where cos(θ) is equal to zero.
The angles in which cos(θ) is equal to zero are 90 degrees and 270 degrees.
Therefore, the angle between vectors A and B is either 90 degrees or 270 degrees.