Write the direction-cosines of the line joining the points (1, 0, 0) and (0, 1, 1).
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For any two vectors →aand →bwe always have ∣→a→˙b∣≤∣→a∣∣→b∣(Cauchy-Schwartz inequality).
If with reference to the right handed system of mutually perpendicular unit vectors i^,j^and k^, →α=3i^−j^,→β=2i^+j^−3k^, then express →βin the from →β=→β1+→β2, where \displaystyle-
A girl walks 4 km towards west, then she walks 3 km in a direction 30oeast of north and stops. Determine the girls displacement from her initial point of departure.
Find the projection of the vector i^−j^on the vector i^+j^
Find the value of x for which x(i^+j^+k^)is a unit vector.
In triangle ABC (Figure), which of the following is not true: (A) AB+BC+CA=0 (B) AB+BC−AC=0 (C) AB+BC−CA=0 (D) AB−CB+CA=0
Find the magnitude of two vectors aand bhaving the same magnitude and such that the angle between them is 60∘and their scalar product is 21.
Evaluate the product (3a−5b)⋅(2a+7b)