A simple question about vector in grade one of senior high school (1) If vector a and B have opposite directions and | a | > b |, then a + B and a have the same direction (2) If the direction of vector a and B is opposite, and | a | > b |, then a - B and a + B have the same direction (3) If vector a and B have the same direction and | a | B |, then a - B and a have opposite directions (4) If vector a and B have the same direction and | a | B |, then a - B and a + B have opposite directions How many are right? How do you feel all right

A simple question about vector in grade one of senior high school (1) If vector a and B have opposite directions and | a | > b |, then a + B and a have the same direction (2) If the direction of vector a and B is opposite, and | a | > b |, then a - B and a + B have the same direction (3) If vector a and B have the same direction and | a | B |, then a - B and a have opposite directions (4) If vector a and B have the same direction and | a | B |, then a - B and a + B have opposite directions How many are right? How do you feel all right

It's all right (just make a sketch on the paper) or something like this
Let B = Ka (K be a constant)
a+b=(1+k)a,a-b=(1-k)a
By comparison, we can see (the direction is related to the positive and negative of K, 1 + K, 1-k)
I suggest you take another look at the definition of vector, especially the module and direction of vector
It's very basic

Let's have a vector problem
1. Several vectors with different starting points but same direction and equal modules are equal vectors
2. If a and B are non-zero vectors and the direction is opposite, then the module of A-B is equal to the module of a plus the module of B
3. There is a unique real number n such that a = Nb ←→ a ‖ B
(←→ equivalent)
One of them is wrong, can you help me find out. I want to say thank you!

The third mistake... It has to be B, it's a non-zero vector

Judge which of the following propositions are true:
If a and B are normal vectors of plane α and β, then a ‖ B & lt; = & gt; α ‖ β
If a and B are normal vectors of plane α and β respectively, then α⊥ β & lt; = & gt; a · B = 0
If n is the normal vector of plane α and B is coplanar with α, then B · n = 0
If the normal vectors of two planes are not perpendicular, the two planes must not be parallel
Which are true, please attach reasons

If a and B are normal vectors of plane α and β, then a ‖ B α ‖ β, it is possible that α and β coincide
If a and B are normal vectors of plane α and β respectively, then α⊥ β a · B = 0, true
If n is the normal vector of plane α and B is coplanar with α, then B · n = 0, true
If the normal vectors of two planes are not perpendicular, the two planes must not be parallel

1. If a is parallel to B, then the projection of a on B is | a|
2. If a is perpendicular to B, then a &; b = (A &; b) ^ 2
(both a and B are vectors)

Wrong. The projection of a on B is the scalar product of a and B divided by the module of B. because a and B are parallel, the scalar product of a and B is equal to the product of a and B module. If a and B are in the same direction, it is a positive sign, but if they are in the opposite direction, it is a negative sign. So it is not necessarily a|
If. A and B are perpendicular, then the product of a and B is equal to 0