If ĀX B(vector)= 0, can you say that (a) Ā=B(vector), (b) Ā is not equal to B(vector) ?
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Answer:
∵∣
a
+
b
∣=∣
a
∣
⇒∣
a
+
b
∣
2
=∣
a
∣
2
⇒(
a
+
b
).(
a
+
b
)=∣
a
∣
2
⇒
a
.
a
+
a
.
b
+
b
.
a
+
b
.
b
=∣
a
∣
2
⇒∣
a
∣
2
+2
a
.
b
+
b
.
b
=∣
a
∣
2
[∵
a
.
b
=
b
.
a
]
⇒2.
a
.
b
+
b
.
b
=0
⇒(2
a
+
b
).
b
=0
⇒(2
a
+
b
) is perpendicular to
b
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