Question #141897
Find the semi vertical angle of a cone with axis x/1=y/2=z/3 and x-axis is the generator?
1
Expert's answer
2020-11-02T20:57:48-0500

x1=y2=z3 direction vector a(1,2,3)\frac{x}{1}=\frac{y}{2}=\frac{z}{3}\text{ direction vector }\vec{a}(1,2,3)

axis X direction vector i(1,0,0)\text{axis }X\text{ direction vector }\vec{i}(1,0,0)

The desired angle is the angle between straight lines or their direction vectors\text{The desired angle is the angle between straight lines or their direction vectors}

cosφ=aiai=111+4+9\cos{\varphi}=\frac{\vec{a}*\vec{i}}{\vert{\vec{a}}\vert*\vert{\vec{i}}\vert}=\frac{1}{1*\sqrt{1+4+9}}

cosφ=113;φ74°\cos{\varphi}=\frac{1}{\sqrt{13}};{\varphi}\approx74\degree

Answer:cosφ=113;φ74°cos{\varphi}=\frac{1}{\sqrt{13}};{\varphi}\approx74\degree


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS