Class CBSE Class 12 Mathematics Vector Algebra Q #817
KNOWLEDGE BASED
APPLY
1 Marks 2023 MCQ SINGLE
The magnitude of the vector 6î - 2î + 3ê is
(A) 1
(B) 5
(C) 7
(D) 12
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Correct Answer: C

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Detailed Solution

Step 1: Identify the vector components

The given vector is v = 6î - 2ĵ + 3k̂. Here, the components are x = 6, y = -2, and z = 3.

Step 2: Apply the magnitude formula

The magnitude of a vector v = aî + bĵ + ck̂ is given by the formula: $$|v| = \sqrt{a^2 + b^2 + c^2}$$

Step 3: Substitute and calculate

Substitute the values into the formula: $$|v| = \sqrt{(6)^2 + (-2)^2 + (3)^2}$$ $$|v| = \sqrt{36 + 4 + 9}$$ $$|v| = \sqrt{49}$$ $$|v| = 7$$

Final Answer: 7

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because it requires the student to recall the definition of vector magnitude and apply the algebraic formula to specific numerical components.
Knowledge Dimension: PROCEDURAL
Justification: The student must follow a specific sequence of mathematical operations (squaring, summing, and square-rooting) to arrive at the solution.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. This is a foundational problem from the chapter 'Vector Algebra' designed to test basic proficiency in vector operations.
||KEY:C

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