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P,Q and R are three points such that vec (PQ)=2a+5b vec (PR)=6a+15b a

User Shanta
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If P is at (0, 0), then Q would be at (2, 5), and R would be at (6, 15). You can choose different values for
x_p and y_p to find other sets of coordinates for P, Q, and R.

To find the coordinates of points P, Q, and R, given the vector representations of PQ and PR as 2a + 5b and 6a + 15b respectively, we need to express the coordinates of these points in terms of a and b. Let's do this step by step:

1. Start with point P. Let's denote the coordinates of P as
(x_p, y_p, z_p). We can express the vector PQ as follows:


PQ = (x_q - x_p) a + (y_q - y_p) b + (z_q - z_p) c

Since we don't have information about c, we can assume it's zero unless specified otherwise. So, we'll focus on the first two components:


2a + 5b = (x_q - x_p) a + (y_q - y_p) b

Now, we can equate the coefficients of a and b to find
x_q - x_p and y_q - y_p:

Equating coefficients of a:


2 = x_q - x_p ...(1)

Equating coefficients of b:


5 = y_q - y_p ...(2)

2. Next, let's move on to point R. Denote the coordinates of R as
(x_r, y_r, z_r). We can express the vector PR as follows:


PR = (x_r - x_p) a + (y_r - y_p) b + (z_r - z_p) c

Again, we'll focus on the first two components:


6a + 15b = (x_r - x_p) a + (y_r - y_p) b

Equating coefficients of a:


6 = x_r - x_p ...(3)

Equating coefficients of b:


15 = y_r - y_p ...(4)

3. Now, we have three equations (equations 1, 2, and 3) to solve for
x_p, y_p, and x_q. We can start by solving equations 1 and 2 for x_q and y_q:

From equation 1:
x_q = 2 + x_p

From equation 2:
y_q = 5 + y_p

4. Next, we'll use equations 3 and 4 to solve for
x_r and y_r:

From equation 3:
x_r = 6 + x_p

From equation 4: x_r = 6 + x_p
x_r = 6 + x_p

5. At this point, we have expressions for
x_q, y_q, x_r, and y_r in terms of x_p and y_p. Now, you can choose arbitrary values for
x_p and y_p, and you can calculate the corresponding values for
x_q, y_q, x_r, and y_r using the expressions derived in steps 3 and 4.

For example, let's say you choose
x_p = 0 and y_p = 0:

From step 3:


x_q = 2 + 0 = 2 \\ y_q = 5 + 0 = 5

From step 4:


x_r = 6 + 0 = 6\\ y_r = 15 + 0 = 15

User EdNdee
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