Related InterviewSolutions

• If the position vectors of the points P and Q are 2 i + 3j + 4k and 3 i – 2 j – 3 k , find the direction cosines of the vector vector PQ and hence prove that,Cos2α + Cos2β + Cos2γ = 1 
• Using Vectors ,prove that the points ( 2, -1 , 3 ) , ( 3, -5 , 1 ) and ( -1 , 11 , 9 ) are collinear.
• Find the angle between the vectors (a + b & a - b) if vector |a| = vector |b|. 
• If vector (a x b ) x c) = vector (a x ( b x c) , then prove that either vector a is parallel to vector c or vector b is perpendicular to both vector(a , c) 
• The vector −A is: A. greater than Vector A in magnitude B. less than Vector A in magnitude C. in the same direction as Vector A D. in the direction opposite to Vector AE. perpendicular to vector A
• If the magnitude of the sum of two vectors is less than the magnitude of either vector, then: A. the scalar product of the vectors must be negative B. the scalar product of the vectors must be positive C. the vectors must be parallel and in opposite directionsD. the vectors must be parallel and in the same direction E. none of the above
• If the magnitude of the sum of two vectors is greater than the magnitude of either vector, then: A. the scalar product of the vectors must be negative B. the scalar product of the vectors must be positive C. the vectors must be parallel and in opposite directions D. the vectors must be parallel and in the same direction E. none of the above
• Prove that (i) vector |a + b|2 + vector |a + b|2 = 2 vector { |a |2 + |b |2} (ii) vector |a + b|2 - vector |a + b|2 = 4 vector (a • b)
•  prove that, ∑  vector (a x ( b x c)) = 0
• Define a null vector ( or Zero vector )