Class CBSE Class 12 Mathematics Vector Algebra Q #555
KNOWLEDGE BASED
APPLY
1 Marks 2024 AISSCE(Board Exam) MCQ SINGLE
If \(|\vec{a}|= 2\) and \(-3\le k\le2\), then \(|\vec{k}\vec{a}|\in\):
(A) [-6, 4]
(B) [0, 4]
(C) [4, 6]
(D) [0, 6]
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AI Tutor Explanation

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Step-by-Step Solution

Given: \(|\vec{a}| = 2\) and \(-3 \le k \le 2\).

We need to find the range of \(|k\vec{a}|\).

Using the property of scalar multiplication of vectors, we have \(|k\vec{a}| = |k||\vec{a}|\).

Substituting the given value of \(|\vec{a}|\), we get \(|k\vec{a}| = |k|(2) = 2|k|\).

Since \(-3 \le k \le 2\), we need to find the range of \(|k|\).

The minimum value of \(|k|\) is 0 (when \(k = 0\)) and the maximum value of \(|k|\) is 3 (when \(k = -3\)).

Therefore, \(0 \le |k| \le 3\).

Multiplying by 2, we get \(0 \le 2|k| \le 6\).

Thus, \(0 \le |k\vec{a}| \le 6\).

Correct Answer: [0, 6]

AI Suggestion: Option D

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Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student needs to apply the properties of scalar multiplication of vectors and the modulus function to find the range of the given expression.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of scalar multiplication of vectors and how the modulus function affects the range of possible values.
Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of vector algebra concepts as covered in the textbook.

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