Vector Algebra
Vector Algebra
nta_pyq_2025_jan
Grade 12
Question:
Let a \pi 3 \to + 2\tob and 3a . If \lambdaa \to - \lambda\tob are perpendicular to each other, then the number of values of \lambda in [-1, 3] is :
Step-by-Step Solution
Key Concept: Apply the core result for dot product, cross product and projections and simplify using the given constraints.
^ ^ ⋅ b = a 1 2 (3) ^ ^ ^ + 2 b) ⋅ (3a Now (\lambdaa ^ - \lambda b) = 0 2 ^ ^ ^ ^ ^ ⋅ a 3\lambdaa ^ - \lambda a^ ⋅ b + 6a ^ ⋅ b - 2\lambda b ⋅ b = 0 2 \lambda 3\lambda - + 3 - 2\lambda = 0 2 2 \lambda - 2\lambda - 6 = 0 \lambda = 1 $\pm$ \sqrt7 \Rightarrow number of values = 0
Correct Answer: 3