Assignment No. 02 CS602 – Computer Graphics Fall 2011

Question                                      20 marks

We have two vectors V1 = (1, 2, 3) and V2 = (4, 5, 6).

Using these vectors evaluate the following.

1.    V1norm =?                                

|V1| = sqrt(1² +2² + 3²)

|V1| =sqrt(14)

|V1| = 3.74

V1_norm = V1 / |V1| = (1+2+ 3) / 3.74

V1_norm = (1 / 3.74, 2 / 3.74, 3 / 3.74)

V1 _norm = (0.27, 0.53, 0.80)

2.    V1 + V2 =?   

V1 + V2 = (V1_x + V2_x, V1_y + V2_y, V1_z + V2_z)   

V1 + V2 = (1 + 4, 2 + 5, 3 + 6)

V1+V2 = (5, 7, 9)

                        

3.    V1.V2 =?        

V1.V2=  (V1_x V2_x ) + (V1_y V2_y ) + (V1_z V2_z)

V1 . V2 = (1 * 4) + ( 2 * 5) + ( 3 * 6)

V1.V2 =4 + 10 + 18

V1 . V2 =32

                         

4.    V1 X V2 =?                                  8 marks

V1 X V2 =(V1y V2z – V1z V2y , V1z V2x - V1x V2z , V1xV2y - V1y V2x )

= (2*6) - (3*5) , (3*4)-(1*6) , (1*5)-(2*4)

= 12 -15 , 12 – 6 , 5 – 8

= -3 , 6 , -3