Three Dimensional Geometry

Q1.The direction cosines of a line are defined as the cosines of the angles the line makes with:

• AThe three coordinate planes
• BThe positive directions of the coordinate axes
• CAny three mutually perpendicular lines
• DThe origin

Q2.The direction ratios of the line joining points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) may be taken as:

• Ax₁+x₂, y₁+y₂, z₁+z₂
• Bx₂-x₁, y₂-y₁, z₂-z₁
• Cx₁x₂, y₁y₂, z₁z₂
• D(x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2

Q3.Two lines have direction ratios 1,-1,-2 and 3,-5,-4. Find the angle between them.

• Acos⁻¹(1/2)
• Bcos⁻¹(√2/3)
• Cπ/3
• Dcos⁻¹(16/√(6×50))

Q4.If l, m, n are the direction cosines of a line, which relation is always satisfied?

• Al + m + n = 1
• Bl² + m² + n² = 0
• Cl² + m² + n² = 1
• Dl × m × n = 1

Q5.If the lines (x-1)/(-3) = (y-2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z-6)/(-5) are perpendicular, find k.

• Ak = -10
• Bk = -1/10
• Ck = 10
• Dk = 1/10