Let a,band c be three non-zero vectors such that no two of them are collinear and (a×b)×c=31∣c∣∣∣b∣∣∣a∣. If θis the angle between vectors band cthen a value of sinθis :
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Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (5,7).
Find the position vector of the mid point of the vector joining the points P(2, 3, 4) andQ(4,1,2).
Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ are 31,31,31.
Find the angle between the vectors i^−2j^+3kand 3i^−2j^+k
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Given that ab˙=0and a×b=0. What can you conclude about the vectors aand b.
Show that the vector i^+j^+k^is equally inclined to the axes OX, OY and OZ.
If a,b,c are unit vectors such that a+b+c=0find the value of a⋅b+b⋅c+c⋅a.