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Question 12 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Aug. 9, 2023 by

If a =4i ˆ+6j ˆ and b =3j ˆ+4k ˆ, then the vector form of the component of a  along b  is

(a) 18/5 (3i ˆ+4k ˆ )                            (b) 18/25 (3j ˆ+4k ˆ )

(c) 18/5 (3i ˆ+4k ˆ )                            (d) 18/25(4i ˆ+6j ˆ)

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Transcript

Now, Vector component of 𝑎 ⃗ along 𝑏 ⃗ = Projection × Unit vector of 𝒃 ⃗ = 𝟏/("|" 𝒃 ⃗"|" ) (𝑎 ⃗. 𝑏 ⃗) × 𝑏 ⃗/(|𝑏 ⃗|) = ((𝑎 ⃗". " 𝑏 ⃗)/〖\ |𝑏 ⃗|〗^2 ) 𝑏 ⃗ ) Now, 𝒂 ⃗ = 4𝑖 ˆ+6𝑗 ˆ = 𝟒𝒊 ˆ+𝟔𝒋 ˆ + 0 𝒌 ˆ 𝒃 ⃗ = 3𝑗 ˆ+4𝑘 ˆ = 0𝒊 ˆ + 𝟑𝒋 ˆ+𝟒𝒌 ˆ Finding 𝒂 ⃗. 𝒃 ⃗ (𝒂 ⃗. 𝒃 ⃗) = (4 × 0) + (6 × 3) + (0 × 4) = 0 + 18 + 0 = 18 Magnitude of 𝑏 ⃗ = √(02+32+42) |𝒃 ⃗ | = √(0+9+16) = √25 = 5 Now, Vector component of 𝑎 ⃗ along 𝑏 ⃗ = ((𝑎 ⃗". " 𝑏 ⃗)/〖\ |𝑏 ⃗|〗^𝟐 ) 𝑏 ⃗ = 18/〖\ 5〗^𝟐 (3𝑗 ˆ+4𝑘 ˆ) = 𝟏𝟖/𝟐𝟓 (𝟑𝒋 ˆ+𝟒𝒌 ˆ ) So, the correct answer is (b)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.