Class CBSE Class 12 Mathematics Vector Algebra Q #562
COMPETENCY BASED
APPLY
1 Marks 2025 AISSCE(Board Exam) MCQ SINGLE
A student tries to tie ropes, parallel to each other from one end of the wall to the other. If one rope is along the vector \(3\hat{i}+15\hat{j}+6\hat{k}\) and the other is along the vector \(2\hat{i}+10\hat{j}+\lambda\hat{k}\), then the value of \(\lambda\) is :
(A) 6
(B) 1
(C) \(\frac{1}{4}\)
(D) 4
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Step-by-Step Solution

Since the ropes are parallel, the vectors representing them must be proportional. Therefore, we can write:

\[ \frac{3}{2} = \frac{15}{10} = \frac{6}{\lambda} \]

From the first two ratios, we have \(\frac{3}{2} = \frac{3}{2}\), which confirms that the vectors are indeed parallel.

Now, we can use the first and third ratios to solve for \(\lambda\):

\[ \frac{3}{2} = \frac{6}{\lambda} \]

Cross-multiplying, we get:

\[ 3\lambda = 12 \]

Dividing both sides by 3, we find:

\[ \lambda = 4 \]

Correct Answer: 4

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 concept of parallel vectors to find the unknown value lambda.
Knowledge Dimension: CONCEPTUAL
Justification: The question requires understanding the concept of parallel vectors and their properties to determine the value of lambda.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. The question requires the application of vector concepts in a practical scenario, testing the student's ability to apply their knowledge rather than just recall facts.

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