Vector Algebra
Vectors in 2D and 3D, dot and cross products, applications.
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Take a full mock →Q1 · Vector Algebra · EASY
If vector a = 3i + 4j and vector b = 5i + 12j, find the magnitude of vector a + b.
Q2 · Vector Algebra · EASY
Two vectors P and Q have magnitudes 3 and 4 respectively. If the angle between them is 60 degrees, what is the value of their dot product P · Q?
Q3 · Vector Algebra · MEDIUM
If a = 2i + 3j - k and b = i - 2j + 3k, find the vector a - 2b.
Q4 · Vector Algebra · MEDIUM
If vectors a = i + 2j + 3k and b = 3i + 4j + 5k, find the magnitude of their cross product a × b.
Q5 · Vector Algebra · HARD
Three vectors a, b, and c are such that a + b + c = 0. If |a| = 3, |b| = 5, and |c| = 7, find the value of a · b + b · c + c · a.