# Describe how the dot product can be used to determine

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13. Describe how the dot product can be used to determine whether two vectors are perpendicular. Create a question with vectors in 3-space to illustrate this property. Be sure to solve the question as well. (5 marks)
u∙v = ( 2 ) ( 5 ) + ( 6 ) ( 1 ) + ( 1 ) (− 4 ) u∙v = 10 6 4 u∙v = 0 these 2 vectorsare perpendicular Task 4: Application Questions 14. Given l 1 =(6,−1,0)+ t (3,1,−4) and l 2 =(4,0,5)+ s (−1,1,5) , find the intersection of l and l 2 . (7 marks) 1
( 5 ) × 3 −( 3 t 3 s = 3 ) s = 5 4 ( 4 ) 3 t ( 5 4 ) =− 2 t = 1 4 ( 1 ) L.S. = 6 + 3 ( 1 4 ) ¿ 21 4 R.S. = 4 −( 5 4 ) ¿ 21 4 L.S.= R.S therefore there is a p.o.i. l 1 = ( 6, 1,0 ) 1 4 ( 3,1, 4 ) 3 4 , 1 4 , 1 ¿ ( 6, 1,0 ) ¿ ¿ ( 6 3 4 , 1 1 4 , 0 + 1 ) ¿ ( 21 4 , 5 4 , 1 )
l 2 = ( 4,0,5 ) 5 4 (− 1,1,5 ) ¿ ( 4,0,5 ) −( 5 4 , 5 4 , 25 4 ) ¿ ( 4 + 5 4 , 0 5 4 , 5 25 4 ) ¿ ( 21 4 , 5 4 , 1 ) isthe ponitof ¿ 15.Find the vector equation of the line of intersection of the following two planes: 4 x +3 y −2 z +7=0 and x −2 y +5 z −1=0 (7 marks)
Input y value x = 2 ( 2 z 3 11 ) 5 z 1 x =− z 17 / 11 Let z=t x =− t 17 / 11 y = 2 t 3 / 11 z = t ( x, y ,z ) = ( 17 11 , 3 11 , 0 ) + t (− 1,2,1 )
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