3D Geometry – JEE Main Practice Test

Q1. Let P(10, −2, −1) and Q be the foot of the perpendicular drawn from R(1,7,6) on the line joining (2, −5, 11) and (−6, 7, −5). Then PQ is:

Q2. In tetrahedron ABCD, AB ⟂ AC ⟂ AD. Areas of ΔABC, ΔACD, ΔADB are 5, 6, 7 respectively. Area of ΔBCD is:

Q3. Let OP = γ. Angle between OQ and x-axis is θ and between OP and z-axis is φ. Distance of P from x-axis is:

Q4. Line L₁ passes through (1,2,3) parallel to z-axis and L₂ through (λ,5,6) parallel to y-axis. If shortest distance is 3, then square of distance of (λ₁,λ₂,7) from L₁ is:

Q5. Shortest distance between (x−3)/4 = (y+7)/(−11) = (z−1)/5 and (x−5)/3 = (y−9)/(−6) = (z+2)/1 is:

Q6. If shortest distance between (x−λ)/−2 = (y−2)/1 = (z−1)/1 and (x−√3)/1 = (y−1)/−2 = (z−2)/1 is 1, then sum of all possible values of λ is:

Q7. Distance of point (7,10,11) from the line (x−4)/1 = (y−4)/0 = (z−2)/3 along the line (x−9)/2 = (y−13)/3 = (z−17)/6 is:

Q8. The line coplanar with (x+3)/−3 = (y−1)/1 = (z−5)/5 is:

Q9. OA = 2i + 2j + k and OB = 2i + 4j + 4k. If internal bisector of ∠AOB meets AB at C, then OC is:

Q10. In ΔABC, AC = 6, B = (1,2,3) and A, C lie on (x−6)/3 = (y−7)/2 = (z−7)/−2. Area of ΔABC is: