By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2024 Maths, question 68

Topic: Analytical geometry

Passage · Q67 to Q68

Let SS be the line of intersection of two planes x+y+z=1x+y+z=1 and 2x+3y−4z=82x+3y-4z=8.

Q68

If ⟨l,m,n⟩⟨l,m,n⟩ are direction cosines of SS, then what is the value of 43(l2−m2−n2)43(l^{2}-m^{2}-n^{2})?

  1. (a) 66Correct answer
  2. (b) 55
  3. (c) 44
  4. (d) 11

Solution.

Answer: (a) 66

  1. Normalise the direction (−7,6,1), whose squared length is 86.
  2. Then l²−m²−n²=(49−36−1)/86=12/86.
  3. Multiplication by 43 gives 6; reversing the line direction leaves these squares unchanged.