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 Feb. 10, 2025 by Teachoo

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)

[MCQ] If a = 4i + 6j, b = 3j + 4k, then vector component of a along b - CBSE Class 12 Sample Paper for 2024 Boards

part 2 - Question 12 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

part 3 - Question 12 - CBSE Class 12 Sample Paper for 2024 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

Next: Question 13 Important → Share on WhatsApp

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)

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 15 years. He provides courses for Maths, Science and Computer Science at Teachoo

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular