Three Dimensional Geometry

Q1.The value of p such that lines (1-x)/3 = (7y-14)/2p = (z-3)/2 and (7-7x)/3p = (y-5)/1 = (6-z)/5 are at right angles is:

• Ap = 7
• Bp = 7/11
• Cp = 70/11
• Dp = 11/7

Q2.Lines in space that are neither parallel nor intersecting are called:

• AConcurrent lines
• BCoplanar lines
• CSkew lines
• DPerpendicular lines

Q3.The Cartesian equation of a line through point (x₁, y₁, z₁) with direction cosines l, m, n is:

• A(x-x₁)/l = (y-y₁)/m = (z-z₁)/n
• B(x+x₁)/l = (y+y₁)/m = (z+z₁)/n
• Clx + my + nz = 0
• Dx/l = y/m = z/n

Q4.A line makes equal angles with all three coordinate axes. What is each direction cosine?

• A1/2
• B±1/√2
• C±1/√3
• D1/3

Q5.The vector equation of a line passing through point with position vector a⃗ and parallel to vector b⃗ is:

• Ar⃗ = b⃗ + λa⃗
• Br⃗ = a⃗ + λb⃗
• Cr⃗ = a⃗ × b⃗
• Dr⃗ = λ(a⃗ + b⃗)