Let's check each statement in turn: Statement (I): "If either |
→
a
|=0 or |
→
b
|=0, then
→
a
â‹…
→
b
=0." - If one of the vectors is the zero vector, say
→
a
=
→
0
, then for any
→
b
→
0
â‹…
→
b
=0 - Hence (I) is true. Statement (II): "If
→
a
×
→
b
=
→
0
, then
→
a
is perpendicular to
→
b
." - Recall |
→
a
×
→
b
|=|
→
a
||
→
b
|sin‌θ, where θ is the angle between them. −
→
a
×
→
b
=
→
0
means sin‌θ=0, so θ=0 or π : the vectors are parallel (or one is zero), not perpendicular. - Hence (II) is false. Conclusion: Statement (I) is true, Statement (II) is false.