Cambridge Additional Mathematics

Vectors (Chapter 11) 281 Now consider the vector from point A to point B. We say that: ² ¡! AB is the vector whichoriginatesat A ...

282 Vectors (Chapter 11) All vectors in the plane can be described in terms of the base unit vectorsiandj. For example: a=3i¡j b ...

1 Vectors (Chapter 11) 283 NEGATIVE VECTORS ¡! AB and ¡! BA have the same length, but they have opposite directions. We say that ...

284 Vectors (Chapter 11) 4 Write in component form and illustrate using a directed line segment: a i+2j b ¡i+3j c ¡ 5 j d 4 i¡ 2 ...

Vectors (Chapter 11) 285 Example 3 Self Tutor Findkgiven that μ ¡^13 k ¶ is a unit vector. Since μ ¡^13 k ¶ is a unit vector, q ...

286 Vectors (Chapter 11) Example 4 Self Tutor If a= μ 1 ¡ 3 ¶ and b= μ 4 7 ¶ , find a+b. Check your answer graphically. a+b= μ 1 ...

Vectors (Chapter 11) 287 SCALAR MULTIPLICATION Ascalaris a non-vector quantity. It has a size but no direction. We can multiply ...

288 Vectors (Chapter 11) Example 7 Self Tutor If p=3i¡ 5 j and q=¡i¡ 2 j, find jp¡ 2 qj. p¡ 2 q=3i¡ 5 j¡2(¡i¡ 2 j) =3i¡ 5 j+2i+4 ...

Vectors (Chapter 11) 289 8 Suppose a=2i¡j, b=i+3j, and c=¡ 4 i. Find: a a+b b 3 b+c c a¡c d 2 b¡a e jc+2aj f j¡ 2 bj 9 Suppose a ...

290 Vectors (Chapter 11) Example 8 Self Tutor Given points A(¡ 1 ,2),B(3,4), and C(4,¡5), find the position vector of: a B from ...

Vectors (Chapter 11) 291 3 [PQ] is the diameter of a circle with centre C. a Find ¡! PC. b Hence find the coordinates of Q. 4 AB ...

292 Vectors (Chapter 11) are parallel vectors of different length. Two non-zero vectors areparallelif and only if one is a scala ...

Vectors (Chapter 11) 293 Example 11 Self Tutor If a=3i¡j, find: a a unit vector in the direction ofa b a vector of length 4 unit ...

294 Vectors (Chapter 11) When we apply vectors to problems in the real world, we often consider the combined effect when vectors ...

Vectors (Chapter 11) 295 ii jfj^2 +jcj^2 =jsj^2 ) jfj^2 +0: 52 =1: 52 ) jfj^2 =2 ) jfj¼ 1 : 41 In these conditions, Jacques’ act ...

DEMO A fixed point() R any point() O origin() line b a r 296 Vectors (Chapter 11) 5 An aeroplane needs to fly due east from one ...

Vectors (Chapter 11) 297 Example 13 Self Tutor A line passes through the point A(1,5) and has direction vector μ 3 2 ¶ . Describ ...

298 Vectors (Chapter 11) 2 A line passes through (¡ 1 ,4) with direction vector μ 2 ¡ 1 ¶ a Write parametric equations for the l ...

Vectors (Chapter 11) 299 If an object has initial position vectoraand moves with constant velocityb, its position at timetis giv ...

300 Vectors (Chapter 11) Example 15 Self Tutor An object is initially at (5,10) and moves with velocity vector 3 i¡j metres per ...