Ex 10.2

Ex 10.2, 1

Ex 10.2, 2

Ex 10.2, 3 Important

Ex 10.2, 4

Ex 10.2, 5 Important

Ex 10.2, 6

Ex 10.2, 7 Important

Ex 10.2, 8

Ex 10.2, 9

Ex 10.2, 10 Important

Ex 10.2, 11 Important

Ex 10.2, 12

Ex 10.2, 13 Important

Ex 10.2, 14

Ex 10.2, 15 Important

Ex 10.2, 16

Ex 10.2, 17 Important You are here

Ex 10.2, 18 (MCQ) Important

Ex 10.2, 19 (MCQ) Important

Last updated at April 21, 2021 by Teachoo

Hello! Teachoo has made this answer with days (even weeks!) worth of effort and love. Since your board exams are coming, why not help Teachoo create more videos and content by supporting us? Please click on this link to make a donation

Hello! Teachoo has made this answer with days (even weeks!) worth of effort and love. Since your board exams are coming, why not help Teachoo create more videos and content by supporting us? Please click on this link to make a donation

Ex 10.2, 17 Show that the points A, B and C with position vectors, 𝑎 ⃗ = 3𝑖 ̂ − 4 𝑗 ̂ − 4𝑘 ̂, 𝑏 ⃗ = 2𝑖 ̂ − 𝑗 ̂ + 𝑘 ̂ and 𝑐 ⃗ = 𝑖 ̂ − 3 𝑗 ̂ − 5𝑘 ̂ , respectively form the vertices of a right angled triangle. Position vectors of vertices A, B, C of triangle ABC are 𝑎 ⃗ = 3𝑖 ̂ − 4𝑗 ̂ − 4𝑘 ̂, 𝑏 ⃗ = 2𝑖 ̂ − 1𝑗 ̂ + 1𝑘 ̂ 𝑐 ⃗ = 1𝑖 ̂ − 3𝑗 ̂ − 5𝑘 ̂ We know that two vectors are perpendicular to each other, i.e. have an angle of 90° between them, if their scalar product is zero. So, if (CA) ⃗. (AB) ⃗ = 0, then (CA) ⃗ ⊥ (AB) ⃗ & ∠ CAB = 90° Now, (AB) ⃗ = 𝑏 ⃗ − 𝑎 ⃗ = (2i ̂ − 1j ̂ + 1k ̂) − (3i ̂ − 4j ̂ − 4k ̂) = (2 − 3) i ̂ + (−1 + 4) j ̂ + (1 + 4) k ̂ = –1i ̂ + 3j ̂ + 5k ̂ (BC) ⃗ = 𝑐 ⃗ − 𝑏 ⃗ = (1i ̂ − 3j ̂ − 5k ̂) − (2i ̂ − 1j ̂ + 1k ̂) = (1 − 2) i ̂ + (−3 + 1) j ̂ + (−5 − 1) k ̂ = −1i ̂ − 2j ̂ − 6k ̂ (CA) ⃗ = 𝑎 ⃗ − 𝑐 ⃗ = (3i ̂ − 4j ̂ − 4k ̂) − (1i ̂ − 3j ̂ − 5k ̂) = (3 − 1) i ̂ + (−4 + 3) j ̂ + (−4 + 5) k ̂ = 2i ̂ − 1j ̂ + 1k ̂ Now, (𝐀𝐁) ⃗ . (𝐂𝐀) ⃗ = (–1i ̂ + 3j ̂ + 5k ̂) . (2i ̂ − 1j ̂ + 1k ̂) = (−1 × 2) + (3 × −1) + (5 × 1) = (−2) + (−3) + 5 = −5 + 5 = 0 So, (AB) ⃗.(CA) ⃗ = 0 Thus, (AB) ⃗ and (CA) ⃗ are perpendicular to each other. Hence, ABC is a right angled triangle.