Question

OAN, OMB, APB and MPN are straight lines and AN = 20A.

M is the midpoint of OB.
OA = a
OB = b
AP = KAB where k is a scalar quantity.
Express AB and MN in terms of a and b.
Express MP in terms of a, b and k.
Finally, find the value of k.

Answer 1

To express AB in terms of a and b, use the fact that M is the midpoint of OB. To express MN in terms of a and b, use the fact that A and N lie on the same straight line. To express MP in terms of a, b, and k, use the fact that AP = KAB.

Step-by-step explanation:

In the given figure, OAN, OMB, APB, and MPN are straight lines and AN = 20A. M is the midpoint of OB. OA = a and OB = b. AP = KAB, where k is a scalar quantity.

To express AB in terms of a and b, we use the fact that M is the midpoint of OB. So, AB = 2OM = 2(OA + AM) = 2(a + b/2) = 2a + b.

To express MN in terms of a and b, we know that A and N lie on the same straight line. So, we can use the fact that AN = 20A. Therefore, MN = AN - AM = 20A - (OA + AM) = 20A - (a + b/2).

To express MP in terms of a, b, and k, we use the fact that AP = KAB. Therefore, MP = AP - AM = KAB - (OA + AM) = KAB - (a + b/2).

To find the value of k, we need more information or a given value for AP. Without that information, we cannot determine the value of k.