Class CBSE Class 12 Mathematics Vector Algebra Q #1728
COMPETENCY BASED
APPLY
1 Marks 2026 AISSCE(Board Exam) MCQ SINGLE
If $(3\hat{i}-2\hat{j}+5\hat{k})\times(4\hat{i}+p\hat{j}+q\hat{k})=\vec{0}$ then the values of p and q are :
(A) $p=-\frac{2}{3}, q=\frac{5}{3}$
(B) $p=-\frac{8}{3}, q=\frac{20}{3}$
(C) $p=\frac{20}{3}, q=-\frac{8}{3}$
(D) $p=0, q=0$
Prev Next
Correct Answer: B

AI Tutor Explanation

Powered by Gemini

Detailed Solution

Step 1: Understand the Condition

Two vectors are collinear if their cross product is the zero vector. Given that the cross product of (3, -2, 5) and (4, p, q) is 0, the vectors must be proportional.

Step 2: Set up Proportionality

Since the vectors are parallel, their components must be in the same ratio: $$ \frac{4}{3} = \frac{p}{-2} = \frac{q}{5} $$

Step 3: Solve for p

Using the ratio: $$ \frac{p}{-2} = \frac{4}{3} $$ $$ p = -2 \times \frac{4}{3} = -\frac{8}{3} $$

Step 4: Solve for q

Using the ratio: $$ \frac{q}{5} = \frac{4}{3} $$ $$ q = 5 \times \frac{4}{3} = \frac{20}{3} $$

Final Answer: p = -8/3, q = 20/3

AI generated content. Review strictly for academic accuracy.

Pedagogical Audit
Bloom's Analysis: This is an APPLY question because the student must utilize the geometric property of the cross product (collinearity) to solve for unknown variables.
Knowledge Dimension: PROCEDURAL
Justification: The question requires the application of a specific algorithm (ratio of components) derived from the definition of vector cross products.
Syllabus Audit: In the context of CBSE Class 12, this is classified as COMPETENCY. It tests the conceptual understanding of vector algebra beyond mere calculation, requiring the student to recognize the relationship between parallel vectors.

More from this Chapter

MCQ_SINGLE
Vector of magnitude 3 making equal angles with x and y axes and perpendicular to z axis is
SA
The position vectors of vertices of $\Delta$ ABC are $A(2\hat{i}-\hat{j}+\hat{k}),$ $B(\hat{i}-3\hat{j}-5\hat{k})$ and $C(3\hat{i}-4\hat{j}-4\hat{k})$ Find all the angles of $\Delta$ AВС.
VSA
If A, B and C be three non-collinear points such that $\vec{AB}=\hat{i}+2\hat{j}-\hat{k}$ and $\vec{AC}=2\hat{i}-3\hat{j}$, then find the area of $\Delta ABC$.
MCQ_SINGLE
The value of m for which the points with position vectors $-\hat{i} - \hat{j} + 2\hat{k}$, $2\hat{i} + m\hat{j} + 5\hat{k}$ and $3\hat{i} + 11\hat{j} + 6\hat{k}$ are collinear, is
MCQ_SINGLE
The magnitude of the vector 6î - 2î + 3ê is
View All Questions