prove law of cosins using parallelogram method of vector addition?
Answers
If two vectors are acting simultaneously at a point, then it can be represented both in magnitude and direction by the adjacent sides drawn from a point. Therefore, the resultant vector is completely represented both in direction and magnitude by the diagonal of the parallelogram passing through the point.
Answer:
Parallelogram law of vector addition states that
if two vectors are considered to be the adjacent sides of a parallelogram, then the resultant of the two vectors is given by the vector that is diagonal passing through the point of contact of two vectors.
Proof:
Let
A
and
B
are the two vectors be represented by two lines
OP
and
OQ
drawn from the same point. Let us complete the parallelogram and name it as OPTQ. Let the diagonal be
OT
.
Since
PT
is equal and parallel to
OQ
, therefore, vector
B
can also be represented by
PT
.
Applying the triangle's law of vector to triangle OPT.
OT
=
OP
+
PT
⇒
R
=
A
+
B
.
(proved).
