11.Three Dimensional Geometry Quiz

What are the direction cosines of a line AB?

• (x2 - x1), (y2 - y1), (z2 - z1)

• (x2 - x1), (y2 - y1), (z2 - z1)

• (x2 - x1)^2, (y2 - y1)^2, (z2 - z1)^2

• (x2 - x1)/√(y2 - y1), (z2 - z1)

What do skew lines in space contain?

• Neither parallel nor intersecting lines

• Lines with equal direction cosines

• Intersecting lines

• Parallel lines

What is the angle between skew lines?

• It varies

• 45 degrees

• 90 degrees

• 60 degrees

What is the equation of a line through a point (x1, y1, z1) with direction cosines l, m, n?

• (x - x1)/l = (y - y1)/m = (z - z1)/n

• (x - x1) = l(y - y1) = m(z - z1) = n

• (x - x1) + l = (y - y1) + m = (z - z1) + n

• (x - x1) - l = (y - y1) - m = (z - z1) - n

What is the shortest distance between two lines?

• (x - x1)/a1 - (y - y1)/b1 - (z - z1)/c1 = (x - x2)/a2 - (y - y2)/b2 - (z - z2)/c2

• (x - x1)/a1 + (y - y1)/b1 + (z - z1)/c1 = (x - x2)/a2 + (y - y2)/b2 + (z - z2)/c2

• (x - x1)/a1 = (y - y1)/b1 = (z - z1)/c1 + (x - x2)/a2 = (y - y2)/b2 = (z - z2)/c2

• (x - x1)/a1 = (y - y1)/b1 = (z - z1)/c1 and (x - x2)/a2 = (y - y2)/b2 = (z - z2)/c2

What is the distance between parallel lines?

• |b(x(a2 - a1))|/|c|

• |b(x(a2 - a1))|/|b|

• |b(x(a2 - a1))|/|a|

• |b(x(a2 - a1))|/|a + b + c|