CBSE Class 12 Sample Paper for 2024 Boards
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CBSE Class 12 Sample Paper for 2024 Boards
Last updated at August 14, 2026 by Teachoo
![[MCQ] If a = 4i + 6j, b = 3j + 4k, then vector component of a along b - CBSE Class 12 Sample Paper for 2024 Boards](https://cdn.teachoo.com/68c3a689-0170-4e13-95ec-64d8f34ea314/slide27.jpg)
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)
