4 The plane contains the line , where , and is parallel to the line , where . (i) Find the vector equation of in scalar product form. [2] (ii) Find the position vector of the foot of the perpendicular from the point to the plane . [3] Find the position vector of the point , which is the reflection of about .[2] (iii) (iv) Given that the angle between , where , and the plane , where , is , find the value of [2] a. (v) Find the line of intersection between the planes and . [1] (vi) has equation , . Given that , and have no points in common, describe the geometrical relationship between the three planes. What can be said the values of and [3] b c? Solution: (i) (ii) Method 1: , for some Since is the intersection point of line and plane, N AN Method 2: , where (iii) (iv)
4 The plane contains the line , where , and is parallel to the line , where . (i) Find the vector equation of in scalar product form. [2] (ii) Find the position vector of the foot of the perpendicular from the point to the plane . [3] (iii) Find the position vector of the point , which is the reflection of about .[2] (iv) Given that the angle between , where , and the plane , where , is , find the value of a. [2] (v) Find the line of intersection between the planes and . [1] (vi) has equation , . Given that , and have no points in common, describe the geometrical relationship between the three planes. What can be said the values of b and c? [3] Solution: (i) (ii) Method 1: , for some Since N is the intersection point of line AN and plane, Method 2: , where (iii) (iv)