Vectors and scalars; addition of vectors; components in two and three dimensions; scalar and vector products; scalar and vector triple products.
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Q1 · Vector Algebra · EASY
If vectors a and b are such that |a| = 3, |b| = 4, and a · b = 6, then the angle between vectors a and b is:
Q2 · Vector Algebra · MEDIUM
Let a = 2i + j - k and b = i - 2j + 3k. The magnitude of the vector (a × b) is:
Q3 · Vector Algebra · MEDIUM
The position vectors of points A, B, C are i + 2j + 3k, 3i + 4j + 7k, and -3i - 2j - 5k respectively. These three points are:
Q4 · Vector Algebra · MEDIUM
If a, b, c are three non-coplanar vectors and p = (a × b) · c, q = (b × c) · a, r = (c × a) · b, then:
Q5 · Vector Algebra · HARD
Let a = i + j + k, b = i - j + k, and c = i + 2j - k. A vector perpendicular to both a and c and making an obtuse angle with b is: