A parallelogram is formed with a and b as the sides. Let 1d and 2d be the diagonals of the parallelogram. The value of a2 + b2 is
Answers
Answer:Let θ be the angle between
a
&
b
The long diagonal of the parallelogram is the vector sum of two sides and short diagonal is vector difference of two sides.
Given...
d
1
=
a
+
b
,
d
2
=
a
−
b
d
1
2
=a
2
+b
2
+2abcosθ
d
2
2
=a
2
+b
2
−2abcosθ
d
1
2
+d
2
2
=2(a
2
+b
2
)
a
2
+b
2
=(d
1
2
+d
2
2
)/2
Answer:
Explanation:
Answer:Let θ be the angle between
a
&
b
The long diagonal of the parallelogram is the vector sum of two sides and short diagonal is vector difference of two sides.
Given...
d
1
=
a
+
b
,
d
2
=
a
−
b
d
1
2
=a
2
+b
2
+2abcosθ
d
2
2
=a
2
+b
2
−2abcosθ
d
1
2
+d
2
2
=2(a
2
+b
2
)
a
2
+b
2
=(d
1
2
+d
2
2
)/2