11 Two vectors
212 Show that the sum and difference of two perpendicular vectors of equal lengths are
also perpendicular and of the same length.
43 explain
Answers
Answered by
2
Answer:
Consider two ⊥ vectors of equal magnitude.
Sum =
a
+
b
∣
∣
∣
∣
a
+
b
∣
∣
∣
∣
=
a
2
+b
2
Difference =
a
−
b
∣
∣
∣
∣
a
−
b
∣
∣
∣
∣
=
a
2
+b
2
Let be angle b/w the vectors cosθ=
∣a
2
+b
2
∣∣a
2
−b
2
∣
(
a
+
b
)(
a
−
b
)
=
a
2
+b
2
a
2
−b
2
=0
⇒θ=90
0
.
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Answer:
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