8/19/2019 QS025 Tugasan Vector

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VECTOR

1. Given  jick  jibk  jia     2,,2  . Find

(a) a vector that perpendicular to both a and b  

(b) cba   .)(    

[7 marks]

2. Given k  jir k  jiqk  ji p          1530,23,5510  . Find

(a) 

, if  p and q are perpendicular .(b)    , if  p and q are parallel

[7 marks]

8/19/2019 QS025 Tugasan Vector

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3. A plane1  passes through three points P (1, -3, 2) , Q(2, -3, 1) and R(3 , -2 , 9)

(a) Find an equation of the plane.

(b) Calculate the acute angle between the plane1 and the plane 2 :   2123     z  y x  

[10 marks]

4. The vector equation of a straight line M is given by )4(2   k  ji sk ir    . The point

Q(3 ,  ,   ) lies on the straight line M .

(a)  Determine the values of   and   .

(b) 

A plane  passes through the point Q and perpendicular to the vector k  ji   2 .Find a vector and Cartesian equation of the plane .

(c)  The straight line M intersects the plane 1782     z  y x at point H . Find the

coordinate of H. 

[13 marks]

8/19/2019 QS025 Tugasan Vector

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5. The parametric equation of 2 straight lines are given by

t  z t  yt  xl    21,24,3:1    

 s z  s y s xl      4,3,1:2  

(a) 

Show that the point (2, -6, 1) lies on both the straight lines.(b)  Find the Cartesian equation of plane containing this 2 lines.

(c)  Calculate the acute angle between the plane described in (b) and the plane

1355     z  y x  

[13 marks]