In direct proportion `a_1/b_1` = `a_2/b_2`

In case of inverse proportion a_2 __ b_2

If the equation of the locus of a point equidistant from the points (a_1,b_1) and (a_2,b_2) is (a_1-a_2)x+(b_2+b_2)y+c=0 , then the value of C is

Statement 1 : veca = 3 veci + p vecj +3veck and vecb = 2veci + 3vecj + qveck are parallel vectors if p = 9//2 and q =2 . Statement 2 : If veca= a_1 veci + a_2 vecj + a_3 veck and vecb = b_1 veci + b_2 vecj + b_3veck are parallel, then (a_1)/(b_1) = (a_2)/(b_2)= (a_3)/(b_3) .

If the points (a_1, b_1),\ \ (a_2, b_2) and (a_1+a_2,\ b_1+b_2) are collinear, show that a_1b_2=a_2b_1 .

If a_mhati+b_mhatj+c_mhatk m=1,2,3 are pairwise perpendicular unit vectors then |[a_1,b_1,c_1] , [a_2,b_2,c_2] , [a_3,b_3,c_3]| is equal to

Let A={a_1,a_2,a_3,.....} and B={b_1,b_2,b_3,.....} are arithmetic sequences such that a_1=b_1!=0, a_2=2b_2 and sum_(i=1)^10 a_i=sum_(i=1)^15 b_j , If (a_2-a_1)/(b_2-b_1)=p/q where p and q are coprime then find the value of (p+q).

If (b_2-b_1)(b_3-b-1)+(a_2-a_1)(a_3-a_1)=0 , then prove that the circumcenter of the triangle having vertices (a_1,b_1),(a_2,b_2) and (a_3,b_3) is ((a_2+a_3)/(2),(b_2+b_3)/(2)) .

If the line a_1 x + b_1 y+ c_1 = 0 and a_2 x + b_2 y + c_2 = 0 cut the coordinate axes in concyclic points, prove that : a_1 a_2 = b_1 b_2 .

Let a=2hati+3hatj-6hatk, b=2hati-3hatj+6hatk and c=-2hati+3hatj+6hat(k), Let a_1 be the projection of a on b and a_2 be the projection of a_1 and c . Then Q. a_1, b is equal to

Prove by vector method that (a_1b_1+a_2b_2+a_3b_3)^2lt+(a_1^2+a_2^2+a_3^2)(b_1^2+b_2^2+b_3^2)