Decide 2

Decide whether points A[-2, -5], B[4, 3] and C[16, -1] lie on the same line

Correct result:

x =  0

Solution:

u=(4(2),3(5))=(6,8) v=(16(2),1(5))=(18,4)  s=u v=uvcosα  cosα=c  c=6 18+8 462+82 182+420.7593  c0  x=0u=(4-(-2), 3-(-5))=(6, 8) \ \\ v=(16-(-2), -1 -(-5))=(18, 4) \ \\ \ \\ s=u \cdot \ v=|u||v| \cos α \ \\ \ \\ \cos α=c \ \\ \ \\ c=\dfrac{ 6 \cdot \ 18+8 \cdot \ 4 }{ \sqrt{ 6^2+8^2 } \cdot \ \sqrt{ 18^2+4^2 } } \doteq 0.7593 \ \\ \ \\ c \ne 0 \ \\ \ \\ x=0



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Ziacka
don't lie on same line

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Two vectors given by its magnitudes and by included angle can be added by our vector sum calculator.
See also our trigonometric triangle calculator.

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