Point T is the midpoint of a straight line AB. Given the position vectors of A and T are i - j + k and 2i + 1 ½ k respectively, find the position vector of B in terms of i, and k
T = A+(B-A)/2 = (A+B)/2
B = 2T-A
so B = (3, 1, 2)
To find the position vector of point B, we can utilize the fact that the midpoint of a straight line divides it into two equal halves. In this case, point T is the midpoint of the line AB.
Let's assume the position vector of point B to be b. Since T is the midpoint of AB, we can use the midpoint formula to find the position vector of B:
T = (A + B)/2
Let's substitute the given position vectors into the formula:
(2i + 1/2k) = (i - j + k + b)/2
To simplify the equation, we can multiply both sides of the equation by 2:
2(2i + 1/2k) = 2(i - j + k + b)/2
4i + k = i - j + k + b
Next, we can group the like terms:
4i + k = i + k - j + b
To isolate the position vector b, we can subtract i and k from both sides of the equation:
3i + j = b
Therefore, the position vector of point B is b = 3i + j.