I need to get the equation of a line that passes through the point Q(6, 3, 2) and intersects: $$L: (1, -1, 4) + t(0, -1, 1)$$ and forms an angle of 60°
What I did so far:
The direction vector of L is A and the director vector of L_1(the line I need to get) is B. Because they intersect and with the dot product:
$$A\cdot B = ||A||\cdot||B||Cos(a)$$ $$a = 60°$$ $$A = (0, -1, 1)$$ $$B = (b_1, b_2, b_3)$$
Another vector I can get is C, that goes from the starting point of L to Q:
$$C = (5, 4, -2)$$
I tried 2 things from there. Because all 3 dots can be in the same plane, I used cross product of vectors like this;
$$C x B = C x A$$ $$C x B = (2, -5, -5)$$ $$C x A = (-b_1 - b_2, -b1, -b1)$$
With this I get the the b_1 = 5. But I need another equation for the other 2.
The other thing I tried is working with the triangle. All the angles are 60°. But I didn't make any important progress.
Any ideas? Thank you.