Find the magnitude of the vector $v = 3 i + 4 j + 12 k$ .

easy 1 mark Class 12 · Mathematics · Vector Algebra

Answer

The correct answer is 13 — Step 6: Conclude the magnitude is $13$ .

Step-by-step solution

Step 1: Write the magnitude formula $∣ v ∣ = v_{x}^{2} + v_{y}^{2} + v_{z}^{2}$ .
Step 2: Substitute the components: $∣ v ∣ = 3^{2} + 4^{2} + 1 2^{2}$ .
Step 3: Compute the squares: $3^{2} = 9$ , $4^{2} = 16$ , $1 2^{2} = 144$ .
Step 4: Add them: $9 + 16 + 144 = 169$ .
Step 5: Take the square root: $169 = 13$ .
Step 6: Conclude the magnitude is $13$ .

Common mistake: Squaring the components incorrectly or forgetting to square one of them.

Concept tested: Magnitude of a vector