 ## 8.7.4 Vectors, SPM Practice (Question 7 & 8)

Question 7:Diagram below shows quadrilateral OPBC. The straight line AC intersects the straight line PQ at point B. It is given that  OP → = a ˜ ,  OQ → = b ˜ ,  OA → =4 AP → ,  OC → =3 OQ → ,  PB → =h PQ →  and AB → =k AC → . … Read more

## 8.7.3 Vectors, SPM Practice (Question 5 & 6)

Question 5: Diagram below shows a triangle KLM. It is given that KP:PL=1:2, LR:RM=2:1,  KP → =2 x ˜ ,  KM → =3 y ˜ . (a) Express in terms of  x ˜  and  y ˜ , (i)  MP → (ii)  MR → (b) Given  x ˜ =2 i ˜  and  y ˜ =− i ˜ +4 j ˜ , find  | MR | → . … Read more

## 8.7.2 Vector, Long Questions (Question 3 & 4)

Question 3: In diagram below, PQRS is a quadrilateral. PTS and TUR are straight lines.     It is given that PQ → =20 x ˜ ,   PT → =8 y ˜ ,   SR → =25 x ˜ −24 y ˜ ,   PT → = 1 4 PS →   and   TU → = 3 5 … Read more

## 8.7.1 Vectors, Long Questions (Question 1 & 2)

Question 1: The above diagram shows triangle OAB. The straight line AP intersects the straight line OQ at R. It is given that OP= 1 4 OB, AQ= 1 4 AB,  OP → =4 b ˜  and  OA → =8 a ˜ .   (a) Express in terms of   a ˜  and/ or  b ˜ : … Read more

## 8.6.3 Vector Short Questions (Question 6 & 7)

Question 6: The points P, Q and R are collinear. It is given that   P Q → = 4 a ˜ − 2 b ˜  and   Q R → = 3 a ˜ + ( 1 + k ) b ˜ , where k is a constant. Find (a)    the value of … Read more

## 8.6.2 Vector Short Questions (Question 4 & 5)

Question 4: Diagram below shows a parallelogram ABCD with BED as a straight line. Given that  AB → =7 p ˜ ,  AD → =5 q ˜  and DE=3EB, express, in terms of  p ˜  and  q ˜ . (a)  BD → (b)  EC → Solution: (a) Note: for parallelogram, A B → = D C → = 7 p ˜ … Read more

## 8.6.1 Vectors, Short Questions (Question 1 – 3)

Question 1: Given that O (0, 0), A (–3, 4) and B (–9, 12), find in terms of the unit vectors,   i ˜ and   j ˜. (a) A B → (b) the unit vector in the direction of  A B → Solution: (a)  A=(−3,4), thus  OA → =−3 i ˜ +4 j ˜ B=(−9,12), thus  OB … Read more

## 8.5 Vectors in Cartesian Plane

(A) Vectors in Cartesian Coordinates 1. A unit vector is a vector whose magnitude is one unit. 2. A unit vector that is parallel to the x-axis is denoted by  i ˜ while a unit vector that is parallel to the y-axis is denoted by j ˜ . 3. The unit vector can be expressed in … Read more

## 8.4 Expression of a Vector as the Linear Combination of a Few Vectors

8.4 Expression of a Vector as the Linear Combination of a Few Vectors 1. Polygon Law for Vectors P Q → = P U → + U T → + T S → + S R → + R Q → 2. To prove that two vectors are parallel, we must express one of the … Read more

## 8.3.2 Subtraction of Vectors

8.3.2 Subtraction of Vectors The subtraction of the vector b ˜ from the vector  a ˜ is written as  a ˜ − b ˜ . This operation can be considered as the addition of the vector a ˜ with the negative vector of b ˜ . Therefore a ˜ − b ˜ = a ˜ … Read more