CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Q242 Marksdot_products
CBSE Class 12 Mathematics 2026 Supplementary Paper 65(B)/7 · Question 24 (Vector Algebra)
If a+b+c=0 and |a|=3, |b|=5, |c|=7, find the angle between a and b. OR Find the area of the parallelogram with adjacent sides (1,−2,3) and (2,−1,4).
Alternative 1 2 Marks
If a+b+c=0 and |a|=3, |b|=5, |c|=7, find the angle between a and b.
Answer: π/3.
- Square |a+b|=|c|.
- The resulting equation is 9+25+30 cos θ=49.
- Hence cos θ=1/2 and θ=π/3.
Alternative 2 2 Marks
Find the area of the parallelogram with adjacent sides (1,−2,3) and (2,−1,4).
Answer: √38.
- Take the cross product of the sides.
- The product is (−5,2,3), with squared norm 38.
- The area is its norm √38.