(10) A line passes through the point Po(ro, 0) and has gradient m = tan a....

 

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(10) A line passes through the point Po(ro, 0) and has gradient m = tan a. Show that a general point of the line has coordinates (ro + A cos a, yo + Asin a), where A is a parameter. (11) Show that the points with position vectors 3i-5j, 4i+į, 6i+13j are collinear. If the point whose position vector is 5ai + 7aj is also on the line, find the value of a. (12) Find the position vector of the point of intersection of the line joining the points whose position vectors are 5i - 4j and -3i + 4j with the line joining the points whose position vectors are -13i + 4j and -5i + j. (13) Points A, B, C, D in a plane have position vectors a = 6i + 8j, b = 3a/2, c = 6i+3j, d= 5¢/3 respectively. Write down the vector equations of the lines AD and BC and find the position vector of their point of intersection. (14) The straight line L passes through the origin O and is in the direction i+mj. The straight line L' passes through the point A whose position vector is aj and is in the direction i+m'j. Write down the vector equations of L and L' and find the position vector of their point of intersection. %3D (10) A line passes through the point Po(ro, 0) and has gradient m = tan a. Show that a general point of the line has coordinates (ro + A cos a, yo + Asin a), where A is a parameter. (11) Show that the points with position vectors 3i-5j, 4i+į, 6i+13j are collinear. If the point whose position vector is 5ai + 7aj is also on the line, find the value of a. (12) Find the position vector of the point of intersection of the line joining the points whose position vectors are 5i - 4j and -3i + 4j with the line joining the points whose position vectors are -13i + 4j and -5i + j. (13) Points A, B, C, D in a plane have position vectors a = 6i + 8j, b = 3a/2, c = 6i+3j, d= 5¢/3 respectively. Write down the vector equations of the lines AD and BC and find the position vector of their point of intersection. (14) The straight line L passes through the origin O and is in the direction i+mj. The straight line L' passes through the point A whose position vector is aj and is in the direction i+m'j. Write down the vector equations of L and L' and find the position vector of their point of intersection. %3D