Which of the following statements are true?

1)If a×b=0, then a=0 or b=0.
2)The sum of the lengths of two vectors can be equal to the length of the sum of the vectors.
3)If a·b=0, then a=0 or b=0.
4)The scalar product of two vectors is always positive.
5)a·(b×a)=0 for all vectors a and b.
6)If three non-zero vectors add up to zero, a+b+c =0, and a·d=0, b·d=0, then c·d=0.

Question

Which of the following statements are true?

1)If a×b=0, then a=0 or b=0.
2)The sum of the lengths of two vectors can be equal to the length of the sum of the vectors.
3)If a·b=0, then a=0 or b=0.
4)The scalar product of two vectors is always positive.
5)a·(b×a)=0 for all vectors a and b.
6)If three non-zero vectors add up to zero, a+b+c  =0, and a·d=0, b·d=0, then c·d=0.

kenljw · Answer

Assuming aXb is a cross product then it's also zero when the angle between them is 0 degrees
Assuming a.b is the dot product then it's also zero when the angle between them is 90 degrees
|a| + |b| is not equal to a +b
this should narrow it down