Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian.
-8x - 10y + 2z = -10 and -4x - 6y + 5z = -7
A) 0.341 rad
B) 1.230 rad
C) 1.571 rad
D) 0.459 rad

Question

Quizplus · Accepted Answer

First find the normal vectors to the planes: Plane 1: <8, -10, 2> Plane 2: <-4, -6, 5> To find the acute angle between the planes, use the dot product formula: cos(theta) = (normal vector of plane 1) dot (normal vector of plane 2) / (magnitude of normal vector of plane 1) * (magnitude of normal vector of plane 2) Plugging in the values: cos(theta) = ((8) (-4) + (-10) (-6) + (2) (5)) / (sqrt(8^2 + (-10)^2 + 2^2)) * (sqrt((-4)^2 + (-6)^2 + 5^2)) cos(theta) = 0.529 Taking the inverse cosine of both sides: theta = 1.230 rad (rounded to the nearest thousandth)

Use a Calculator to Find the Acute Angle Between the Planes