Chapter 10 Class 12 Vector Algebra
Ex 10.2, 9
Ex 10.2, 10 Important
Ex 10.2, 13 Important
Ex 10.2, 17 Important
Example 14 Important
Example 16 Important
Example 21 Important
Ex 10.3, 2
Ex 10.3, 3 Important
Ex 10.3, 10 Important
Ex 10.3, 13 Important
Ex 10.3, 16 Important
Example 23 Important
Example 24
Example 25 Important
Ex 10.4, 2 Important
Ex 10.4, 5 Important
Ex 10.4, 9 Important
Ex 10.4, 10
Ex 10.4, 11 (MCQ) Important
Example 28 Important
Example 29 Important
Example 30 Important
Misc 6
Misc 12 Important You are here
Misc 13
Misc 15 Important
Misc 19 (MCQ) Important
Chapter 10 Class 12 Vector Algebra
Last updated at April 16, 2024 by Teachoo
Misc 12 Let 𝑎 ⃗ = 𝑖 ̂ + 4𝑗 ̂ + 2𝑘 ̂, 𝑏 ⃗ = 3𝑖 ̂ − 2𝑗 ̂ + 7𝑘 ̂ and 𝑐 ⃗ = 2𝑖 ̂ − 𝑗 ̂ + 4𝑘 ̂ . Find a vector 𝑑 ⃗ which is perpendicular to both 𝑎 ⃗ and 𝑏 ⃗ and 𝑐 ⃗ ⋅ 𝑑 ⃗ = 15 . Given 𝒂 ⃗ = 𝑖 ̂ + 4𝑗 ̂ + 2𝑘 ̂ 𝒃 ⃗ = 3𝑖 ̂ - 2𝑗 ̂ + 7𝑘 ̂ 𝒄 ⃗ = 2𝑖 ̂ + 𝑗 ̂ + 4𝑘 ̂ Let 𝒅 ⃗ = x𝒊 ̂ + y𝒋 ̂ + z𝒌 ̂ Since 𝒅 ⃗ is perpendicular to 𝑎 ⃗ and 𝑏 ⃗ 𝑑 ⃗ . 𝑎 ⃗ = 0 & 𝑑 ⃗ . 𝑏 ⃗ = 0 𝒅 ⃗ . 𝒂 ⃗ = 0 (x𝑖 ̂ + y𝑗 ̂ + z𝑘 ̂). (1𝑖 ̂ + 4𝑗 ̂ + 2𝑘 ̂) = 0 (x × 1) + (y × 4) + (z × 2) = 0 x + 4y + 2z = 0 𝒅 ⃗ . 𝒃 ⃗ = 0 (x𝑖 ̂ + y𝑗 ̂ + z𝑘 ̂). (3𝑖 ̂ − 2𝑗 ̂ + 7𝑘 ̂) = 0 (x × 3) + (y × -2) + (z × 7) = 0 3x − 2y + 7z = 0 Also, 𝑐 ⃗ . 𝑑 ⃗ = 15 (2𝑖 ̂ – 1𝑗 ̂ + 4𝑘 ̂). (x𝑖 ̂ + y𝑗 ̂ + z𝑘 ̂) = 15 (2 × x) + (−1 × y) + (4 × 2) = 15 2x − y + 4z = 15 Now, we need to solve equations x + 4y + 2z = 0 3x − 2y + 7z = 0 & 2x − y + 4z = 15 Solving x + 4y + 2z = 0 3x – 2y + 7z = 0 𝑥/(28 − (−4) ) = 𝑦/(6 − 7 ) = 𝑧/(−2 − 12 ) 𝒙/(𝟑𝟐 ) = 𝒚/(−𝟏 ) = 𝒛/(−𝟏𝟒 ) Writing x & y in terms of z ∴ x = 32𝑧/(−14) = (−𝟏𝟔𝒛)/𝟕 & y = (−1𝑧)/(−14) = 𝒛/𝟏𝟒 Putting values of x and y in (3) 2x – y + 4z = 15 2 ((−16𝑧)/7 ) − (𝑧/14 ) + 4z = 5 (−32)/7 z − 1/14 z + 4/1 z = 15 ((−64 − 1 + 56))/14 z = 15 (−9)/14 z = 15 z = 15 × 14/(−9) z = (−𝟕𝟎)/𝟑 Putting value of z in x & y, x = (−16𝑧)/7 = (−16)/7 × (−70)/3 = 𝟏𝟔𝟎/𝟑 y = 𝑧/14 = 1/14 × (−70)/3 = (−𝟓)/𝟑 Therefore, the required vector 𝑑 ⃗ = x𝑖 ̂ + y𝑗 ̂ + z𝑘 ̂ = 160/3 𝑖 ̂ − 5/3 𝑗 ̂ – 70/3 𝑘 ̂ = 𝟏/𝟑 (160𝒊 ̂ − 5𝒋 ̂ – 70𝒌 ̂) Note: Answer given in the book is incorrect If we have made any mistake, please email at [email protected]