Is AB perpendicular to BC where A =(2,0,-1), B=(4,3,-6) and C = (9,3,-4)
AB = B - A = (4,3,-6)- (2,0,-1) = (2 , 3 , -5)BC = C - B = (9,3,-4) - (4,3,-6) = (5, 0 , 2)
If perpendicular "AB dot BC" should equal zeroAB dot BC = (2,3,-5) dot (5,0,2) = (2x5) + (3x0) + (-5x2) = 10 + 0 +(-10) = 0Therefore AB is perpendicular to BC
SU
Related Maths A Level answers
All answers ▸How do I show two lines are skew?
How many solutions are there of the equation a+b+c=12, where a,b,c are non-negative integers?
The equation of a line is y=3x – x^3 a) Find the coordinates of the stationary points in this curve, stating whether they are maximum or minimum points b) Find the gradient of a tangent to that curve at the point (2,4)
Show that the line with equation ax + by + c = 0 has gradient -a/b and cuts the y axis at -c/b?