RI 2024 RTT2_Vectors(Worksheet)

RAFFLES INSTITUTION H2 Mathematics (9758) 2024 Year 5 ________________________________________ Y5 H2 Math RTT2 Focus Lesson on Vectors Page 1 of 4 Term 4 RTT2: Post-Promo Revision Lesson Worksheet Session 3: C4A to C4C: Vectors 1 Referred to the origin O, the points A and B have position vectors a and b respectively. The vectors a and b are given by 263a n d 2 ,ppp   aij k b i j k where p is a constant. Find ab a and give a geometrical interpretation of ab a . [2] Find ab and give a geometrical interpretation of ab . [2] Given that ais a unit vector, find the possible value(s) of p . [2] 2 DHS Prelim 9758/2020/01/Q6b modified With reference to the origin O, the points A and B are such that OA   a and OB   b. It is given that 2 3OX   a, 3 4OY   b and the line ON bisects the line XY at the point M. (i) By considering the ratio :XM MY , find the vector OM  in terms of a and b. [1] (ii) Given that :: 1AN NB  and :: 1ON OM k  where  and k are real constants, find the ratio AN : NB. [4] 3 (a) The non-zero vectors a, b and c are such that ab ca . Given that bc , find a linear relationship between a, b and c. [3] (b) The variable vector vij kabc satisfies the equation  3.vi k j  Find the set of vectors v and describe this set geometrically. [3] A B O X N Y M

Raffles Institution H2 Mathematics 2024 Year 5 __________________________________________ Y5 H2 Math RTT2 Focus Lesson on Vectors Page 2 of 4 4 ACJC Promo 9758/2020/Q8 The lines l and m are defined by the equations :( 2 6 3 ) , 13:. 44 l xa y zm a     ri k i j k (i) Given that the lines intersect, show that 6a . [2] (ii) Find the position vector of N, the foot of perpendicular from the point (5, 0,1)A to the line l. [3] (iii) Find the position vector of the two points on l that are 5 units from A. [3] 5 9740/2015/02/Q2 The line L has equation 24 ( 236 ) .    ri j k i j k (i) Find the acute angle between L and the x-axis. [2] The point P has position vector 256 .ij k (ii) Find the points on L which are a distance of (33) from P. Hence or otherwise find the point on L which is closest to P. [5] (iii) Find a cartesian equation of the plane that includes the line L and the point P . [3] 6 JPJC Promo 9758/2020/Q9 modified The plane 1p has equation 10 2 1 , where and are real parameters. 01            r . (i) Find an equation of 1p in the form dr.n . [3] The plane 2p has equation 21 2xyz . (ii) State the relationship between 1p and 2p . [1] The line l has equation 3 2 2 t    r , where t is a real parameter. (iii) Find the acute angle between l and 1p . [2] (iv) Find the foot of perpendicular from the origin to 2p . Hence, or otherwise, find the exact distance bet