Question 10 (OR 1 st question)

Find the area of the parallelogram whose diagonals are represented by the vectors a = 2i  – 3j  + 4k and b = 2i – j + 2k   1. Class 12
2. Solutions of Sample Papers and Past Year Papers - for Class 12 Boards
3. CBSE Class 12 Sample Paper for 2019 Boards

Transcript

Question 10 (OR 1st question) Find the area of the parallelogram whose diagonals are represented by the vectors 𝑎 ⃗ = 2𝑖 ̂ – 3𝑗 ̂ + 4𝑘 ̂ and 𝑏 ⃗ = 2𝑖 ̂ – 𝑗 ̂ + 2𝑘 ̂ Area of parallelogram with diagonals Area = 1/2 |(𝑑_1 ) ⃗×(𝑑_2 ) ⃗ | Given Diagonals of a parallelogram as 𝑎 ⃗ = 2𝑖 ̂ – 3𝑗 ̂ + 4𝑘 ̂ and 𝑏 ⃗ = 2𝑖 ̂ – 𝑗 ̂ + 2𝑘 ̂ Area of the parallelogram = 1/2 |𝑎 ⃗×𝑏 ⃗ | Finding 𝒂 ⃗ × 𝒃 ⃗ 𝑎 ⃗ × 𝑏 ⃗ = |■8(𝑖 ̂&𝑗 ̂&𝑘 ̂@2&−3&4@2&−1&2)| = 𝑖 ̂ ((–3) × 2 – (-1) × 4) − 𝑗 ̂ (2 × 2 − 2 × 4) + 𝑘 ̂ (2 × (-1) − 2 × (-3)) = 𝑖 ̂ (-6 + 4) − 𝑗 ̂ (4 – 8) + 𝑘 ̂ (–2 + 6) = 𝑖 ̂ (−2) - 𝑗 ̂ (−4) + 𝑘 ̂ (4) = –2𝑖 ̂ + 4𝑗 ̂ + 4𝑘 ̂ So, Magnitude of 𝑎 ⃗ × 𝑏 ⃗ = √((−2)2+(4)2+(4)2) |𝑎 ⃗" × " 𝑏 ⃗ | = √(4+16+16) |𝑎 ⃗" × " 𝑏 ⃗ |= √36 |𝑎 ⃗" × " 𝑏 ⃗ |= 6 Thus, Area of the parallelogram = 1/2 |𝑎 ⃗×𝑏 ⃗ | = 1/2 × 6 = 3 square units

CBSE Class 12 Sample Paper for 2019 Boards

Class 12
Solutions of Sample Papers and Past Year Papers - for Class 12 Boards 