Vectors in the same and opposite direction

[sohail queshi]

Homework Statement

which of the vector

V1=(1,2) , V2= (0,1) , V3= (-2,-4) , V4= (-2,1) , V5= (2,4) , V6= (-6,3) are

a) in the same direction
b) in the opposite direction

Homework Equations

The Attempt at a Solution

i tried as follow...
i draw these two vectors on the plan [ (-2,-4) and (2,4)] it gives opposite direction , but i m not conform whether my attempt is right or not...so please help me ..as quick as possible , coz this is my assignment question...tnx in advance

 

[mighty2000]

Hello,

To determine whether two vectors are in the same or opposite direction, you can use the dot product formula. The dot product of two vectors, V1 and V2, is given by V1∙V2 = |V1||V2|cosθ, where θ is the angle between the two vectors.

If the dot product is positive, then the vectors are in the same direction. If it is negative, then they are in the opposite direction. If it is zero, then the vectors are perpendicular.

Using this formula, you can calculate the dot products for V1 and V2, V1 and V3, V1 and V4, V1 and V5, and V1 and V6. If the dot product is positive, then the vectors are in the same direction. If it is negative, then they are in the opposite direction. From your attempt, it seems like you have correctly determined that V3 and V5 are in opposite directions, and V4 and V6 are in the same direction.

Hope this helps! Let me know if you have any further questions.