Let a,b,andc be three non coplanar unit vectors such that the angle between every pair of them is 3π. If a×b+b×x=pa+qb+rc where p,q,r are scalars then the value of q2p2+2q2+r2 is
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Find the value of x for which x(i^+j^+k^)is a unit vector.
Find the area of the triangle with vertices A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5).
If a,b,care mutually perpendicular vectors of equal magnitudes, show that the vector a+b+cis equally inclined to a,b and c.
If either a=0or b=0, then a⋅b=0But the converse need not be true. Justify your answer with an example.
Find angle θbetween the vectors a=i^+j^−k^and b=i^−j^+k^.
Write the direction ratios of the vector →a=i^+j^−2k^and hence calculate its direction cosines.
Find the vector joining the points P(2,3,0)and Q(1,2,4)directed from P to Q.
Find the unit vector in the direction of the vector a=i^+j^+2k^