This document consists of practice questions on the topic Vectors publish by FIITJEE institute.Full description
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Once again keeping a keen ear to the needs of the evolving calculus community, Stewart created this text at the suggestion and with the collaboration of professors in the mathematics department at ...
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In this paper we have established the bounds of the extreme characteristic roots of nlap G and sLap G by their traces. Also found the bounds for n th characteristic roots of nLap G and sLap G . M M Jariya "Results on Characteristic Vectors" Published
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Unit 1, Chapter 1, Scalars and VectorsFull description
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21 questions on vectors covering all that is needed
IB Math HL Matrices and Vectors AnswersFull description
IB Math HL Matrices and VectorsFull description
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AQA Mechanics 1 Kinematics in two dimensions Section 1: Using vectors Exercise 1. Write as a single vector (i) AB BC
(ii) PQ RQ
(iii) AB BC CD
(iv) AC BC BD
(v) PQ SR RQ
2. ABCD is a rectangle. Decide whether the following statements are true or false. (i) AB CD
(ii) AB BC AD DC
3. The diagonals of a parallelogram ABCD intersect at M. If AB p and AD q , express in terms of p and q the vectors (i) BD
(ii) AM
(iii) AC
(iv) MD
4. a, b and c are vectors representing displacements such that a represents 2 km due north, b represents 1 km north west and c represents 2 km due west. Find the magnitudes and directions of (i) 2a (ii) 4b (iii) -a (iv) a + b (v) b - c 5. If AB = 2i – j j, BC = 3i + 4 j and AD = i + 5 j, ABCD is a quadrilateral and M is the mid point of CD, express in terms of i and j the vectors (i) AC
(ii) CD
(iii) DB
(iv) AM
(v) DM
6. Find the components of each of the vectors below in the directions O x and O y. (i) Vector a has magnitude 10 and makes an angle of 50° with the positive direction O x. (ii) Vector b has magnitude 8 and makes an angle of 125° with the positive direction O x. (iii)Vector c has magnitude 4 and makes an angle of -80° with the positive direction O x. 7. A particle accelerates at a constant rate from an initial velocity of 3i j to a final velocity of 5i 3j over 2 seconds. Find the acceleration of the particle . 8. A particle has initial velocity 2i 3j and acceleration of (i) the velocity of the particle after 5 seconds (ii) the displacement of the particle after this time.
i
j . Find
9. A particle moves from point A, which has position vector 3i 5 j , to point B, which has position vector 7i j . When it is at A, it is moving with velocity i 2 j . The journey from A to B takes 4 seconds. (i) Find the acceleration of the particle. (ii) Find the speed of the t he particle when it reaches B.
10. An aeroplane heads due south with a velocity of 300 kmh . It is being blown by a -1 wind with velocity 45 kmh from a bearing of 250 . Find the velocity of the aeroplane relative to the ground.
11. A canal has straight parallel banks 100 m apart. A man rows a boat at 4 ms -1 in a direction perpendicular to the banks. If the canal flows at 1.2 ms -1, find the magnitude of the resultant velocity of the boat and the dista nce downstream that the boat is carried as it crosses from one side to the other. 12. A boy sailing a boat wishes to land on Treasure Island which is due west of his -1 current position. There is a current of 3 kmh flowing from S 28 E. The boy bo y -1 knows that in still water his boat can reach 10 kmh . What course should he steer to reach the island?
