1.

If a,b,c are there given non-coplanar vectors and any arbitrary vector r is in space. Where, Delta_(1) =|{:(r.a,b.a,c.a),(r.b,b.b,a.b),(r.a,b.c,c.c):}|, Delta_(2)=|{:(a.a,r.a,c.a),(a.b,r.b,c.b),(a.c,r.c,c.c):}|, Delta_(3) =|{:(a.a,b.a,r.a),(a.b,b.b,r.b),(a.c,b.c,r.c):}|, Delta=|{:(a.a,b.a,c.a),(a.b,b.b,c.b),(a.c,c.c,c.c):}| The vector r is expressible in the form:

Answer»

`R=Delta_(1)/(2Delta)a + (Delta_(2))/(2Delta)b +(Delta_(3))/(2Delta)c`
`r=(2Delta_(1))/Deltaa+ (2Delta_(2))/Delta b + (2Delta_(3))/(Delta)c`
`r=Delta/Delta_(1) a + Delta/Delta_(2)b+Delta/Delta_(3)c`
`r= Delta_(1)/Delta a + (Delta_(2))/DELTAB+ Delta_(3)/DELTAC`

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