`(bar(a)*bar(i))^(2)+(bar(a)*bar(j))^(2)+(bar(a)*bar(k))^(2)=`

Show that points with p.v bar(a)-2bar(b)+3bar(c ),-2bar(a)+3bar(b)-bar(c ),4bar(a)-7bar(b)+7bar(c ) are collinear. It is given that vectors bara,barb,bar c are non-coplanar.

Let O be the origin and let PQR be an arbitrary triangle. The point S is such that bar(OP)*bar(OQ)+bar(OR)*bar(OS)=bar(OR)*bar(OP)+bar(OQ)*bar(OS)=bar(OQ)*bar(OR)+bar(OP)*bar(OS) Then the triangle PQR has S as its

Observe the following statements : (A) : 10 is the mean of a set of 7 obervations and 5 is the mean of a set of 3 observations. The mean of a combined set is 9. (R ) : If bar(x)_(i)(i = 1,2,…,k) are the means of k - series n_(i)(I = 1,2,3,…,k) respectively, then the combined or composite mean is bar(x) = (n_(1)bar(x)_(1) + n_(2) bar(x)_(2) + ...+ n_(k)bar(x_(k)))/(n_(1)+n_(2)+...+n_(k))

In a regular hexagon ABCDEF, bar(AB) + bar(AC)+bar(AD)+ bar(AE) + bar(AF)=k bar(AD) then k is equal to

Arrange the carbanions, (CH_(3))_(3)bar(C),bar(C)Cl_(3),(CH_(3))_(2)bar(C)H,C_(6)H_(5)bar(C)H_(2) , in order of their decreasing stability

Arrange the carbanions, (CH_(3))_(3)bar(C),bar(C)Cl_(3),(CH_(3))_(2)bar(C)H,C_(6)H_(5)bar(C)H_(2) , in order of their decreasing stability

If |z_(1)|=|z_(2)|=1 , then prove that [{:(,z_(1),-z_(2)),(,bar(z)_(2),bar(z)_(1)):}] [{:(,bar(z)_(1),z_(2)),(,-bar(z)_(2),z_(1)):}]=[{:(,1//2,0),(,0,1//2):}]

For two unimobular complex numbers z_(1) and z_(2) , find [(bar(z)_(1),-z_(2)),(bar(z)_(2),z_(1))]^(-1) [(z_(1),z_(2)),(-bar(z)_(2),bar(z)_(1))]^(-1)

If z_(1)= 3 + 5i and z_(2)= 2- 3i , then verify that bar(((z_(1))/(z_(2))))= (bar(z)_(1))/(bar(z)_(2))

Evaluate 3.bar(2)-0.bar(16)