What is the shear transformation for the vector 3i + 2j?
Answers
The given vector is 3 i + 2 j.
There are two kinds of shear transformation.
1. Horizontal shear(Shear parallel to X axis) 2. Vertical shear(Shear parallel to Y axis.)
As you have not written the shear factor, let suppose the shear factor is k.
1.Horizontal shear(Shear parallel to X axis)→ Shearing will displace this point in right direction,If k is (+),and will move this point in left if k is (-).
Shearing of (3,2) in horizontal direction direction by value k=(3+2 k, 2)
As the point (3,2) moves to a new coordinate(3+2 k,2).Suppose earlier the angle between the point and origin was α i.e tanα,now after shearing it becomes β.So cotangent of β → Cot β is shearing angle.
2. Shearing Vertically(along vertical axis i.e parallel to Y axis)→Shearing the point (3,2) by an amount k along parallel to Y axis in right direction will take it to (3,2+3 k).Shearing will displace this point in right direction.If k is (+),and will move this point in left if k is (-).Cot of angle made by this point with the origin is shearing angle.
Answer:
(3
2)
Step-by-step explanation: