If bc +qr=ca+rp=ab+pq=-1,
show that `|{:(ap,bp,cr),(a,b,c),(p,q,r):}|=0`

If bc+qr=ca+rp=ab+pq=-1 and (abc,pqr!=0) then |[ap,a,p],[bq,b,q],[cr,c,r]| is (A) 1 (B) 2 (C) 0 (D) 3

If a,b,c are non-zero real number such that |(bc,ca,ab),(ca,ab,bc),(ab,bc,ca)|=0, then

Show that |1ab+c1bc+a1ca+b|=0

If a,b,c are in AP show that (i) 1/(bc) ,1/(ca),1/(ab) are in AP.

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 value of |{:(a,b,c),(a.p,b.p,c.p),(a.q,b.q,c.q):}| is:

If a,b,c are in AP, show that (a(b+c))/(bc) , (b (c+a))/(ca), (c(a+b))/(ab) , are also in AP.

If a,b,c are in Ap, show that (i) (b +c-a),(c+a-b) ,(a+b-c) are in AP. (bc -a^(2)) , (ca - b^(2)), (ab -c^(2)) are in AP.