Find the Angle Between the Vectors (10,-9) , (13,-5)

Math
(10,-9) , (13,-5)
The equation for finding the angle between two vectors θ states that the dot product of the two vectors equals the product of the magnitudes of the vectors and the cosine of the angle between them.
u⋅v=|u||v|cos(θ)
Solve the equation for θ.
θ=arc⋅cos(u⋅v|u||v|)
Find the dot product of the vectors.
Tap for more steps…
To find the dot product, find the sum of the products of corresponding components of the vectors.
u⋅v=u1v1+u2v2
Substitute the components of the vectors into the expression.
10⋅13-9⋅-5
Simplify.
Tap for more steps…
Remove parentheses.
10⋅13-9⋅-5
Simplify each term.
Tap for more steps…
Multiply 10 by 13.
130-9⋅-5
Multiply -9 by -5.
130+45
130+45
Add 130 and 45.
175
175
175
Find the magnitude of u.
Tap for more steps…
To find the magnitude of the vector, find the square root of the sum of the components of the vector squared.
(u1)2+(u2)2
Substitute the components of the vector into the expression.
(10)2+(-9)2
Simplify.
Tap for more steps…
Raise 10 to the power of 2.
100+(-9)2
Raise -9 to the power of 2.
100+81
Add 100 and 81.
181
181
181
Find the magnitude of v.
Tap for more steps…
To find the magnitude of the vector, find the square root of the sum of the components of the vector squared.
(u1)2+(u2)2
Substitute the components of the vector into the expression.
(13)2+(-5)2
Simplify.
Tap for more steps…
Raise 13 to the power of 2.
169+(-5)2
Raise -5 to the power of 2.
169+25
Add 169 and 25.
194
194
194
Substitute the values into the equation for the angle between the vectors.
θ=arccos(175(181)⋅(194))
Simplify.
Tap for more steps…
Simplify the denominator.
Tap for more steps…
Combine using the product rule for radicals.
arccos(175181⋅194)
Multiply 181 by 194.
arccos(17535114)
arccos(17535114)
Multiply 17535114 by 3511435114.
arccos(17535114⋅3511435114)
Combine and simplify the denominator.
Tap for more steps…
Multiply 17535114 and 3511435114.
arccos(175351143511435114)
Raise 35114 to the power of 1.
arccos(1753511435114135114)
Raise 35114 to the power of 1.
arccos(17535114351141351141)
Use the power rule aman=am+n to combine exponents.
arccos(17535114351141+1)
Add 1 and 1.
arccos(17535114351142)
Rewrite 351142 as 35114.
Tap for more steps…
Use axn=axn to rewrite 35114 as 3511412.
arccos(17535114(3511412)2)
Apply the power rule and multiply exponents, (am)n=amn.
arccos(175351143511412⋅2)
Combine 12 and 2.
arccos(175351143511422)
Cancel the common factor of 2.
Tap for more steps…
Cancel the common factor.
arccos(175351143511422)
Divide 1 by 1.
arccos(17535114351141)
arccos(17535114351141)
Evaluate the exponent.
arccos(1753511435114)
arccos(1753511435114)
arccos(1753511435114)
Evaluate arccos(1753511435114).
0.36564126
0.36564126
Find the Angle Between the Vectors (10,-9) , (13,-5)

Download our
App from the store

Create a High Performed UI/UX Design from a Silicon Valley.

Scroll to top