Check sibling questions

Ex 10.2, 19 - If a,  bare two collinear vectors, then which

Ex 10.2, 19 - Chapter 10 Class 12 Vector Algebra - Part 2
Ex 10.2, 19 - Chapter 10 Class 12 Vector Algebra - Part 3
Ex 10.2, 19 - Chapter 10 Class 12 Vector Algebra - Part 4

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Ex 10.2, 19 If 𝑎 ⃗ & 𝑏 ⃗ are two collinear vectors, then which following are incorrect: (A) 𝑏 ⃗ = λ𝑎 ⃗, for some scalar λ (B) 𝑎 ⃗ = ±𝑏 ⃗ (C) the respective components of 𝑎 ⃗ and 𝑏 ⃗ are not proportional (D) both the vectors 𝑎 ⃗ & 𝑏 ⃗ have same direction, but different magnitudes. Given, a ⃗ and b ⃗ are collinear We need to check which case is always true Checking (A) 𝑏 ⃗ = λ𝑎 ⃗ If two vectors if a ⃗ and b ⃗ are collinear then b ⃗ = λ𝑎 ⃗ Where λ is any real number ∴ (A) is always correct Checking (B) 𝑎 ⃗ = ±𝑏 ⃗ Let 𝑎 ⃗ = 1i ̂ + 1j ̂ + 1k ̂ 𝑏 ⃗ = −3i ̂ − 3j ̂ − 3k ̂ Here, 𝑎 ⃗ and 𝑏 ⃗ are collinear as direction ratios are proportional. But, 𝑎 ⃗ ≠ ±𝑏 ⃗ So, (B) is not always true Checking (C) (the respective components are not proportional) By definition of collinearity, if a ⃗ and b ⃗ are collinear then b ⃗ = λ𝑎 ⃗ Where λ is any real number Hence, the components of a ⃗ and b ⃗ are always proportional Hence, (C) is incorrect Checking (D) (both 𝑎 ⃗ and 𝑏 ⃗ have same direction, but different magnitudes) Let 𝑎 ⃗ = 1𝑖 ̂ + 1𝑗 ̂ + 1𝑘 ̂ & 𝑏 ⃗ = –3𝑖 ̂ – 3𝑗 ̂ – 3𝑘 ̂ Here, a ⃗ & b ⃗ are collinear as direction ratios are in proportion. But, a ⃗ and 𝑏 ⃗ have opposite direction ∴ (D) is not always true So, (B), (C), (D) are incorrect

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.