I have this question: "If vector c forms an obtuse angle with the OY-axis and is orthogonal to both vectors a = 3i + 2j + 2k and b = 18i - 22j - 5k. Find the component of c if it's norm is 14"
This I can gather:
a dot c = 0 (because they are orthogonal)
b dot c = 0 (because they are orthogonal)
a x b = 0 (because both a and b are orthogonal to c, a and b must be paralell)
|a| = sqrt(17)
|b| = 7sqrt(17)
|a x c| = 119
|a x b| 98sqrt(17)
I know from the equation that if the angle is obtuse with the 0Y axis, the Y component must be negative, so I surmise that c = c1 *i - c2 *j + c3*k
Other than that I'm completely lost, I can't figure out how to find the components of vector c
Writing c as , knowing that and are orthogonal, you know that and knowing that and are othogonal, you know that . Knowing that you know that . You can solve the first two, linear, equations for and as functions of and put those into the last equation to get a quadratic equation for . It's the fact that that quadratic equation has two solutions that requires that additiona information about the angle.