Using the property of determinants and without expanding ` {:[( b+c,q+r,y+z),( c+a,r+p,z+x),( a+b,p+q,x+y) ]:}=2 {:[(a,p,x),( b,q,y),(c,r,z)]:}`

Using the property of determinants and without expanding {:[( x,a,x+a),( y,b,y+b),(z,c,z+c)]:} =0

Prove that the value of determinants is zero: |a-b b-c c-a x-y y-z z-x p-q q-r r-p|

Show that {:|(x+2a,y+2b,z+2c),(x,y,z),(a,b,c)|:} =0

If A= [(2x,2y,2z),(2a,2b,2c),(2p,2q,2r)] and Delta =[(x,y,z),(a,b,c),(p,q,r)] then det A is

Match the following lists (where [x] represents the greatest integer function) and then choose the correct code. Codes : {:(,"a b c d"),((1),"s r q p"),((2),"q p s p"),((3), "s r p q"),((4),"p p q r"):}

The determinant |x p+y x y y p+z y z0x p+y y p+z|=0 if x ,y ,z

The minimum value of P=b c x+c a y+a b z , when x y z=a b c , is

If a ,b ,c are the p t h ,q t h ,r t h terms, respectively, of an H P , show that the points (b c ,p),(c a ,q), and (a b ,r) are collinear.