Elastic Collision of Identical Spheres

[proticks97]

Homework Statement

In a glancing collision between two identical steel spheres, which of the following statements are correct? (Assume this collision is perfectly elastic. Select all that apply.)
1)The velocities of the spheres after the collision in the direction perpendicular to the incoming direction will be equal in magnitude and opposite in direction.
2)The sum of the velocity vectors of the two spheres in the original direction of the incoming sphere after the collision will be equal to that of the incoming sphere.
3)Kinetic energy in this collision will be conserved.
4)Linear momentum will be conserved in this collision

The Attempt at a Solution

I got that 3 and 4 are correct but not sure if 1 and 2 are

 

[BvU]

Heelo Pro, welcome to PF !

You already picked 3 and 4. When you look at the momentum in the direction perpendicular to the incoming direction before the collision, and take 4 into account, what will it be after the collision ? So what does that say about the velocities after the collision in the direction perpendicular to the incoming direction ?
I don't understand 2 at all. If there are 2 phsres coming in, how can they talk about only 1 afterwards ? Can you think of a wasy to let this follow from 3 and/or 4 ? If not, then it's a fake answer.