Find the magnitude and direction angle for the given vector.
12√(2), -12√(2)
i got 24; 315
you know that (1,1) = √2,π/4
so, now you have an angle in QIV, so it is
24,7π/4
To find the magnitude and direction angle of a vector, we can use the following formulas:
Magnitude = √(x^2 + y^2)
Direction angle = arctan(y/x)
Given the vector (12√2, -12√2), we can substitute the values into the formulas:
Magnitude = √((12√2)^2 + (-12√2)^2)
= √(288 + 288)
= √(576)
= 24
Direction angle = arctan((-12√2)/(12√2))
= arctan(-1)
= -45 degrees (or -π/4 radians)
Therefore, the magnitude of the vector is 24 and the direction angle is -45 degrees (or -π/4 radians).