(a) Find the vector Q=[0, a,0] such that the resultant of the vectors: P=[5, 7, 8], Q=[0, a, 0] , R= [0, 3, –3], S= [-6, 7,0] lies in the xz-plane. (b) Choose any two vectors a and b in the three dimensional space R and verify the identity 4 (a · b) = |a+ bl? – la – bl?. (c) Find value(s) of a so that the planes x + 2y + 3z = 6 and a+ ay + z = 0 are orthogonal.

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Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

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Q: Show that the vectors are orthogonal.

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.