Practice Problems Using Cross Product :
Here we are going to see some practice questions using cross product.
(1) Find the magnitude of a vector x b vector, if a vector = 2i vector + j vector + 3k vector and b vector = 3i vector+ 5j vector - 2k vector Solution
(2) Show that
(3) Find the vectors of magnitude 10√3 that are perpendicular to the plane which contains i vector + 2j vector + k vector and i vector + 3j vector + 4k vector Solution
(4) Find the vectors of magnitude 10√3 that are perpendicular to the plane which contains i vector + 2j vector + k vector and i vector + 3j vector + 4k vector Solution
(5) Find the unit vectors perpendicular to each of the vectors a vector + b vector and a vector - b vector where a vector = i vector + j vector + k vector and b vector = i vector + 2j vector + 3k vector Solution
(6) Find the area of the parallelogram whose two adjacent sides are determined by the vectors i vector + 2j vector + 3k vector and 3i vector − 2j vector + k vector. Solution
(7) Find the area of the triangle whose vertices are A(3, - 1, 2), B(1, - 1, - 3) and C(4, - 3, 1). Solution
(8) If a vector, b vector, c vector are position vectors of the vertices A, B, C of a triangle ABC, show that the area of the triangle ABC is (1/2) |a × b + b × c + c × a| vector. Also deduce the condition for collinearity of the points A, B, and C. Solution
(9) For any vector a vector prove that
|a vector × i vector |2+|a vector × j vector|2+|a vector × k vector|2= 2 |a vector|2 Solution
(10) Let a vector, b vector, c vector be unit vectors such that a ⋅ b = a ⋅ c = 0 and the angle between b vector and c vector is π/3. Prove that a vector = ± (2/√3) (b × c) Solution
(11) Find the angle between the vectors 2i vector + j vector − k vector and i vector+ 2j vector + k vector using vector product. Solution
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