MHB What is the angle between vector a and b if a=-4i-2j and b=i-7j?

[karush]

$$a=-4i-2j$$ and $$b=i-7j$$

$$a\cdot b=(-4)(1)+(-2)(-7)=10$$
$$||a||=\sqrt{(-4)^2+(-2)^2}=2\sqrt{5}$$

$$||b||=\sqrt{1^2+(-7)^2}=5\sqrt{2} $$

$$\cos\theta = \frac{10}{10\sqrt{10}}$$ so $$\theta\approx72^o$$

 

[MarkFL]

Re: angle between vector a and b give answer to nearest degree.

Looks good to me! (Sun)

 

[karush]

Re: angle between vector a and b give answer to nearest degree.

Thnx to MHB I make some progress...

 

[HallsofIvy]

Re: angle between vector a and b give answer to nearest degree.

Frankly, it doesn't make much sense to me. You give two complex numbers, a and b, and then immediately take the dot product of two vectors, u and d. Where are u and d defined?
I presume that you are taking u= a and v= b but I don't see why you changed their names.

 

[karush]

Re: angle between vector a and b give answer to nearest degree.

Frankly, it doesn't make much sense to me. You give two complex numbers, a and b, and then immediately take the dot product of two vectors, u and d. Where are u and d defined?
I presume that you are taking u= a and v= b but I don't see why you changed their names.

You're correct, the original problem just uses $a$ and $b$; $u$ and $d$ should not be used.

 

[Prove It]

Re: angle between vector a and b give answer to nearest degree.

I expect it's just a typo, and u is supposed to be a and d is supposed to be b.

 

[HallsofIvy]

Re: angle between vector a and b give answer to nearest degree.

I expect it's just a typo, and u is supposed to be a and d is supposed to be b.

Hey, no fair editing after my post- that makes me look like a fool! (And I was hoping I could keep that quiet.)