Vectors in 2D/3D, dot and cross products, scalar triple product, projections.
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Q1 · Vector Algebra (Class 12) · EASY
If vector a = 2i + 3j - k and vector b = i - 2j + 3k, then find the value of a · b (dot product).
Q2 · Vector Algebra (Class 12) · MEDIUM
The angle between vectors a = i + j + k and b = i - j + k is:
Q3 · Vector Algebra (Class 12) · HARD
If vectors a = 2i + j - k, b = i - 2j + k, and c = 3i + j + 2k, then the scalar triple product [a b c] equals:
Q4 · Vector Algebra (Class 12) · EASY
If vectors ā = 2î + 3ĵ + k̂ and b̄ = î - 2ĵ + 4k̂, then the magnitude of (ā - b̄) is:
Q5 · Vector Algebra (Class 12) · HARD
If ā, b̄, c̄ are three vectors such that |ā| = 2, |b̄| = 3, |c̄| = 4, and ā + b̄ + c̄ = 0̄, then the value of ā·b̄ + b̄·c̄ + c̄·ā is: