Q556: If $\vec{a}=2\hat{i}-\hat{j}+\hat{k}$ and \(\vec{b}=\hat{i...

Class CBSE Class 12 Mathematics Vector Algebra Q #556

KNOWLEDGE BASED

APPLY

1 Marks 2024 AISSCE(Board Exam) MCQ SINGLE

If $\vec{a}=2\hat{i}-\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}-\hat{k}$, then $\vec{a}$ and $\vec{b}$:

(A) collinear vectors which are not parallel

(B) parallel vectors

(D) unit vectors

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Correct Answer: C

AI Tutor Explanation

Step-by-Step Solution

To determine the relationship between vectors $\vec{a}$ and $\vec{b}$, we can calculate their dot product.

The dot product of $\vec{a}$ and $\vec{b}$ is given by: $\vec{a} \cdot \vec{b} = (2\hat{i}-\hat{j}+\hat{k}) \cdot (\hat{i}+\hat{j}-\hat{k})$

Calculating the dot product: $\vec{a} \cdot \vec{b} = (2 \times 1) + (-1 \times 1) + (1 \times -1) = 2 - 1 - 1 = 0$

Since the dot product is 0, the vectors are perpendicular.

Correct Answer: perpendicular vectors

AI Suggestion: Option C

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Pedagogical Audit

Bloom's Analysis: This is an APPLY question because the student needs to apply the concept of dot product to determine the relationship between the two vectors.

Knowledge Dimension: PROCEDURAL

Justification: The question requires the student to follow a specific procedure (calculating the dot product) to arrive at the solution.

Syllabus Audit: In the context of CBSE Class 12, this is classified as KNOWLEDGE. The question directly tests the student's understanding of vector properties and their relationships as covered in the textbook.

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