CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Q242 Marksdot_products
CBSE Class 12 Mathematics 2026 Main Paper 65/5/1 · Question 24 (Vector Algebra)
For a=(2,−3,1), b=(0,4,−2), c=(3,0,2), find λ such that a+λb is perpendicular to c. OR Find the area of triangle ABC if AB=(1,2,−1) and AC=(2,−3,0).
Alternative 1 2 Marks
For a=(2,−3,1), b=(0,4,−2), c=(3,0,2), find λ such that a+λb is perpendicular to c.
Answer: λ=2.
- Set (a+λb)·c=0.
- Compute a·c=8 and b·c=−4.
- Solve 8−4λ=0.
Alternative 2 2 Marks
Find the area of triangle ABC if AB=(1,2,−1) and AC=(2,−3,0).
Answer: √62/2.
- Use half the norm of AB×AC.
- The cross product is (−3,−2,−7), of norm √62.
- Halve the norm to obtain the area.