Question

vector section formula​

Answer 1

Step-by-step explanation:

represented by position vectors OP→ and OQ→, respectively, with respect to origin O. We can divide the line segment joining the points P and Q by a third point R in two ways:

Internally

Externally

If we want to find the position vector OR→ for the point R with respect to the origin O, then we should take both the cases one by one.

Case 1 – R Divides Segment PQ Internally

Take a look at Fig. 1 again. In this figure, if the point R divides PQ→ such that,

mRQ→ = nPR→ … (1)

where ‘m’ and ‘n’ are positive scalars, then we can say that R divides PQ→ internally in the ratio m:n. Now, from the triangles ORQ and OPR, we have

RQ→ = OQ→ – OR→ = b⃗ – r⃗

And, PR→ = OR→ – OP→ = r⃗ – a⃗

Therefore, replacing the values of RQ→ and PR→ in equation (1) above, we get

m(b⃗ – r⃗ ) = n(r⃗ – a⃗ )

Or, r⃗ = mb⃗ +na⃗ m+n … (2)

Hence, the position vector forula of the point R which divides PQ internally in the ratio m:n is,

OR→ = mb⃗ +na⃗ m+n

Answer 2

Answer:

Refer the attachement for better understanding.

Thank you