Show that the points A(2i^−j^+k^),B(i^−3j^−5k^),C(3i^−4j^−4k^)are the vertices of a right angled triangle.
The position vectors of points AandB w.r.t. the origin are a=i^+3j^−2k^, b=3i^+j^−2k^ respectively. Determine vector OP which bisects angle AOB, where P is a point on AB˙
Examine the following vector for linear independence: (1) i+j+k,2i+3j−k,−i−2j+2k (2) 3i+j−k,2i−j+7k,7i−j+13k
Statement 1: If ∣∣a+b∣∣=∣∣a−b∣∣, then a and b are perpendicular to each other. Statement 2: If the diagonal of a parallelogram are equal magnitude, then the parallelogram is a rectangle.