Question

The angle between the lines formed by joining the points 2,−3,−5,1and 7,−10,3is​

Answer 1

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Find the angle between the ...

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Asked on December 20, 2019 by

Amardeep Gameti

Find the angle between the lines joining the points (-1, 2), (3,-5) and (-2, 3), (5,0).

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ANSWER

Here,

m

1

= Slope of line joining (-1,2) and (3,-5)

m

1

=

3+1

−5−2

=

4

−7

m

2

= Slope of line joining (-2,3) and (5,0)

m

2

=

5+2

0−3

=

7

−3

Let θ be the acute angle between the given lines, then

tanθ=

∣

∣

∣

∣

∣

1+m

1

m

2

m

1

−m

2

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

∣

1+(

4

−7

)(

7

−3

)

4

−7

−(

7

−3

)

∣

∣

∣

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

∣

∣

∣

4

7

28

−37

∣

∣

∣

∣

∣

∣

∣

∣

=

∣

∣

∣

∣

∣

49

−37

∣

∣

∣

∣

∣

tanθ=

49

37

θ=tan

−1

(

49

37

)

θ=37.05

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