Question

37.(a) State and illustrate (prove) parallelogram law of vector addition.​

Answer 1

According to the parallelogram law of vector addition if two vectors act along two adjacent sides of a parallelogram(having magnitude equal to the length of the sides) both pointing away from the common vertex, then the resultant is represented by the diagonal of the parallelogram passing through the same common vertex 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).