If x(cap),y(cap),z(cap) are mutually perpendicular unit vectors and ax(cap)+ay(cap)+cz(cap),x(cap)+z(cap) and cx(cap)+cy(cap)+bz(cap) are coplanar,then a,b,c are in A.P a,b,c are in G.P a,b,c are in H.P a,c,b are in G.P

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Amit · Answer

Since x,y,z are mutually perpendicular unit vectors we can consider then i,j,k..Now Write the Scalar triple product of the three vectors i.e; the determinent .. since they are coplanar put this determinent zero and get answer as c²=ab. Hence a,c,b are in GP

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If x(cap),y(cap),z(cap) are mutually perpendicular unit vectors and ax(cap)+ay(cap)+cz(cap),x(cap)+z(cap) and cx(cap)+cy(cap)+bz(cap) are coplanar,then a,b,c are in A.P a,b,c are in G.P a,b,c are in H.P a,c,b are in G.P

If x(cap),y(cap),z(cap) are mutually perpendicular unit vectors and ax(cap)+ay(cap)+cz(cap),x(cap)+z(cap) and cx(cap)+cy(cap)+bz(cap) are coplanar,then

a,b,c are in A.P

a,b,c are in G.P

a,b,c are in H.P

a,c,b are in G.P

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