Show that the points A, B, C with position vectors 2i^–j^+k^,i^–3j^–5k^and3i^–4j^–4k^ respectively, are the vertices of a right-angled triangle. Hence find the area of the triangle.
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Let a=i^+4j^+2k^,b=3i^−2j^+7k^and c=2i^−j^+4k^. Find a vector dwhich is perpendicular to both aand band c. d=15.
Show that ∣a∣b+∣∣b∣∣ais perpendicular to ∣a∣b−∣∣b∣∣a, for any two nonzero vectors a and b.
Find the projection of the vector i^+3j^+7k^on the vector 7i^−j^+8k^
Find ∣∣a−b∣∣,if two vector aand bare such that ∣a∣=2,∣∣b∣∣=3and ab˙=4.
Classify the following measures as scalars and vectors.(i) 5 seconds (ii) 1000 cm3
For given vectors, a=2i^−j^+2k^ and b=−i^+j^−k^ find the unit vector in the direction of the vector a+b.
Find the values of x and y so that the vectors 2i^+3j^and xi^+yj^are equal.