# Vector making obtuse angle with x-axis

Find unit vector making an obtuse angle with x-axis and perpendicular to the plane containing the points $$A(1,2,3), B(2,3,4), C(1,5,7)$$.

I managed to derive the plane containing the points $$A, B, C$$ viz. $$x-4y+3z-2=0$$ but cannot proceed from here.

Hint: for any plane given by the equation $$ax + by + cz + d = 0$$, the vector $$(a, b, c)$$ originating from the origin is perpendicular to the plane. So in your case $$(1, -4, 3)$$ is perpendicular to your plane. Now, it remains for you to answer these questions
• If the unit vector you got above is not obtuse with the $$x$$-axis, how do further modify it so that the new unit vector is? In fact, how do you determine the angles unit vectors make with the $$x$$-axis?
• Yes, that will give you your unit vector. Now, how do you calculate the angle it makes with the $x$-axis? – ZeroXLR Apr 7 at 11:54
• Yes, but don't forget to divide by $\sqrt{26}$ i.e. $(-1, 4, -3) / \sqrt{26}$ is the final answer. – ZeroXLR Apr 7 at 12:02