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 as:

If a,b,c are there given non-coplanar vectors and any arbitrary vector

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 as:
Answer» `r=(r b C)/(2[ABC]) a + [rcb]/(2[abc]) b+ [cab]/(2[abc])`c `r=(2[abc])/[abc]a + (2[rcb])/(abc) b + (2[rab])/[abc]c` `r=1/[abc][(abc)a+(rca)b +(rab)c]` None of these Answer :C

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