Add the following: `ab-bc-ca`, `ca-ab`

Add the following: a-b+ab , b-c+bc ,c-a+ac

If (lna)/(b-c)=(lnb)/(c-a)=(lnc)/(a-b) , prove the following . a^(b^2+bc+c^2).b^(c^2+ca+a^2).c^(a^2+ab+b^2)=1

Add: ab-4a,4b-ab,4a-4b

Using the Properties of determinants, prove the following: {:|(1,1,1),(a,b,c),(bc,ca,ab)|=(a-b)(b-c)(c-a)

Which of the following contains both Ca and Mg ?

In the following figure AB bot BC and angleACB=30^(@), given that BC=sqrt(300)m . The length of AB is:

In the following figure, /_ ABC = 90^(@) and /_ AMP = 90^(@) . Prove that : (I) (II) (CA)/(PA) = (BC)/(MP)

If a,b,c are unit vectors such that a+b+c=0 , then find the value of a.b+b.c+c.a .

Find the proudct (a-b-c) (a ^(2) + b ^(2) + c ^(2) - ab + bc-ca) without actual multiplication.

Using the property of determinants prove that {:|( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) |:} = 3( a+b+c) ( ab+bc+ca)