Question
Find the angle between the vector A=31-j+2k
and the negative y axis
and the negative y axis
Answers
GPT 3.5
To find the angle between vector A and the negative y-axis, we can use the dot product of the two vectors and the formula for the angle between two vectors:
Let the negative y-axis be represented by the vector B = 0-i-0k.
The dot product of vectors A and B is given by:
A · B = (31)(0) + (-1)(-1) + (2)(0) = 1
The magnitude of vector A is given by:
|A| = sqrt((31)^2 + (-1)^2 + (2)^2) = sqrt(972) = 31
The magnitude of vector B is given by:
|B| = sqrt((0)^2 + (-1)^2 + (0)^2) = 1
Using the formula cosθ = A · B / (|A| |B|), we can find the angle θ:
cosθ = 1 / (31 * 1) = 1 / 31
θ = arccos(1 / 31) ≈ 85.47 degrees
Therefore, the angle between vector A and the negative y-axis is approximately 85.47 degrees.
Let the negative y-axis be represented by the vector B = 0-i-0k.
The dot product of vectors A and B is given by:
A · B = (31)(0) + (-1)(-1) + (2)(0) = 1
The magnitude of vector A is given by:
|A| = sqrt((31)^2 + (-1)^2 + (2)^2) = sqrt(972) = 31
The magnitude of vector B is given by:
|B| = sqrt((0)^2 + (-1)^2 + (0)^2) = 1
Using the formula cosθ = A · B / (|A| |B|), we can find the angle θ:
cosθ = 1 / (31 * 1) = 1 / 31
θ = arccos(1 / 31) ≈ 85.47 degrees
Therefore, the angle between vector A and the negative y-axis is approximately 85.47 degrees.