In each of the following problems, components of `vec AB` along X-axis and Y-axis are respectively `a_1` and `a_2`. Find the point B when:
` a _1= -5, a_2= 4, A(7,8)`.

In each of the following problems, components of vec AB along X-axis and Y-axis are respectively a_1 and a_ 2 . Find the point B when: a _1= -2, a_2= -4, A(-1,-2) .

In each of the following problems, components of vec AB along X-axis and Y-axis are respectively a underset 1 and a underset 2 . Find the point B when: a underset 1 = 2, a underset 2 = 3, A(2,-3) .

The vector vec v= vec AB has components 3,-4 and 5 and the point A has the coordinates(2,-3,1). Find the point B.

If A is the point (1,2) and the vector vec AB has components 2 and 6, find the point B.

Let the area of a given triangle ABC be Delta . Points A_1, B_1, and C_1 , are the mid points of the sides BC,CA and AB respectively. Point A_2 is the mid point of CA_1 . Lines C_1A_1 and A A_2 meet the median BB_1 points E and D respectively. If Delta_1 be the area of the quadrilateral A_1A_2DE , using vectors or otherwise find the value of Delta_1/Delta

Find the first five terms of the following sequence and obtain the corresponding series : a_1 = a_2 = 3 , a_n = a_(n-2) + 1 , n ge 3

Find the equation of an ellipse whose major axis is along the y-axis and which passes through the points (2,2) and (1,4).

Let a_1, a_2 ,........ be positive real numbers in geometric progression. For each n, let A_n, G_n, H_n be respectively the arithmetic mean, geometric mean and harmonic mean of a_1,a_2..........a_n . Find an expression ,for the geometric mean of G_1,G_2,........G_n in terms of A_1, A_2,........ ,A_n, H_1, H_2,........,H_n .

Let A(-1, 2, 1) and B(4, 3, 5) be two given points. Find the projection of AB on a line which makes angle 120^(@) and 135^(@) with Yand Z-axes respectively, and an acute angle with X-axis.