Question

Please & TY - Consider the vector " v = (-6, 13) " ?
Consider the vector
http://tinypic.com/r/e80a5s/5
If the text below doesn't make sense, this link shows you the original problem!

Part I: Use the dot product to find the angle (in degrees) between " v = (-6, 13) " and the vector (1,0).
Part II: Writev in the form (l v l cosθl v l sinθ). Express the angle θ in degrees.
Part III: Use the dot product of the vectors " v = (-6, 13) " and " w = (-42, -34) " to determine if they are orthogonal.

Answer 1

Part 1)

Angle between two vectors a and b is given by
cosθ = a . b /|a|*|b|
here a.b =(-6, 13).(1,0) = -6 *1 +13 *0 =-6+0 = -6
|a| = sqrt [(-6)^2 + (13)^2] = sqrt (205)
|b|=sqrt [(1)^2 + 0^2]= sqrt(1)=1

So,
cosθ = -6 /sqrt(205)
θ = arc cos[-6/sqrt(205)] arc cos is same as cos^-1
θ=114.8 degree (one decimal place)
So the angle between both vectors are approximately 114.8 degrees

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Part 2)

for any vector <a,b>, angle θ is given by θ= tan^-1(b/a)
here a = -6 and b=13
θ= tan^-1(13/-6) = 114.8 (approximately)

Now magnitude of vector is |v|= sqrt((-6)^2 + (13)^2) = sqrt(205)
Thus using |v|=sqrt(205) and θ= 114.8
(l v l cosθ, l v l sinθ)= (sqrt(205)* cos 114.8 , sqrt(205)* sin 114.8) answer

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Part 3)

Find the dot product of vectors " v = (-6, 13) " and " w = (-42, -34) "
v.w= (-6)*(-42)+(13)*(-34)=252-442= -192
Since v.w is not equals to zero.
The vector v and w are not orthogonal

Answer 2

@abb0t @dumbcow @genius12 @Hero @zzr0ck3r am I doing this correctly?

Answer 3

looks great

Answer 4

i concur

Answer 5

Thanks everyone! I just wanted to double check