If the vectors AB=3i^+4k^ and AC=5i^−2j^+4k^are the sides of a triangle ABC, then the length of the median through A is
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Three vectors →a, →band →csatisfy the condition →a+→b+→c=→0. Evaluate the quantity μ=→a→˙b+→b→˙c+→⋅→a, if ∣→a∣=1,∣→b∣=4and ∣→c∣=2.
Let a,band cbe three vectors such that ∣a∣=3,∣∣b∣∣=4,∣c∣=5and each one of them being perpendicular to the sum of the other two, find ∣∣a+b+c∣∣.
Write two different vectors having same magnitude.
Find the unit vector in the direction of the vector a=i^+j^+2k^
Find the unit vector in the direction of vector PQ, where P and Q are the points (1, 2, 3) and (4, 5, 6), respectively.
Show that the points A(2i^−j^+k^),B(i^−3j^−5k^),C(3i^−4j^−4k^)are the vertices of a right angled triangle.
Consider two points P and Q with position vectors →OP=3→a−2→band →OQ=→a+→bFind the position vector of a point R which divides the line joining P and Q in the ratio 2:1, (i) internally, and (ii) externally.
For any two vectors a and b, we always have ∣∣a+b∣∣≤∣a∣+∣∣b∣∣