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PLEASE HELP!
Thanks in advance!​

PLEASE HELP! Thanks in advance!​-example-1
User Floris
by
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1 Answer

4 votes

Answer:

10.67 degree.

Explanation:

Note:
The angle between two lines can be found using their direction cosines. The formula is:


\boxed *

where:

  • a and b are the direction cosines of the two lines

  • \theta is the angle between the two lines
  • ||a|| and ||b|| are the magnitudes of a and b

In this case, the direction cosines of the two lines are proportional to 1, 2, 3 and 3, 4, 5.

So, we can write the direction cosines as follows:

a = (1, 2, 3)

b = (3, 4, 5)

The magnitudes of a and b are:


\tt ||a|| = √(1^2 + 2^2 + 3^2) = √(13)


\tt ||b|| = √(3^2 + 4^2 + 5^2)= 5√(2)

Now, we can find the angle between the two lines using the formula above:


\tt cos \: \theta = (1 * 3 + 2 * 4 + 3 * 5)/(√(13) * 5√(2) )=(13√(7))/(35)

The angle theta can be found using the arc cos function or inverse cos function.


\tt \theta =cos^(-1)((13√(7))/(35))=10.67

Therefore, the angle between the two lines is 10.67 degree.

User Kongulov
by
7.8k points

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