Vector Made Easy By Rajesh Kumar Giri
During my college life i faced a lot of problems to solve the questions in vector. I tried to get its solution from my tutor, professor and several help books but i failed. I went through concepts, illustrations, examples and work assignments. I was totally confused but being a struggler find out the best way to solve vector problems and decided to share you. Now it is your turn to rate me after observing the fact. SPECIAL FEATURES *CLEAR-CUT CONCEPTS *STEP BY STEP SOLUTION *COVERING CBSE LATEST SYLLABUS *WORKING ASSIGNMENTS *TOPIC-WISE ILLUSTRATION Contents of the E-book 1. DETERMINATION OF MAGNITUDE OF VECTORS 2. ADDITION OF VECTOR 3. FINDING OUT SCALAR AND VECTOR COMPONENTS 4. FINDING OUT UNIT VECTOR 5. TO PROVE COLLINIARITY OF VECTORS
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AN INSTITUTE FOR YOUR WARDS PERFECTION
VECTORS-AN INTRODUCTION-1
BASIC LEVEL-A(INTRODUCTION TO VECTORS)
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1.For what values of ‘?’, the vectors (2î - 3 j ) and (?î - 6j) are parallel ?
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2.Find the position vector of the centroid of a ?ABC where a , b and c are the position vectors of the vertices A, B and C respectively. |
3.Find position vectors of the points which divides the join of the points 2a - 3b and 3a - 2b externally in the ratio 2:3. |
4.Find the projection of the vector î +3 j +7k on the vector 7î – j + 8k. |
5.Find the area of the parallelogram whose diagonals are 2î - 3j + 4k and -3î + 4j – k |
6.Find the cosine of an acute angle between the vectors 2î - 3j + k and î + j -2 k |
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8.If | a | = 5, | b | = 13 and | a x b | = 25. Find a . b |
9.Find the position vector of the mid point of the vector joining the points P(2,3,4) and Q(4,1,-2) |
10.Find the value of ‘x’ for which x(î + j + k ) is a unit vector. |
11.If the position vector a of the point (5,n) is such that | a | = 13, find the value of n |
12.If the vector a = 2î - 3j and b = -6î + mj are collinear , find the value of m |
13.If a vector makes angles a, ß, ? with x-axis, y-axis, z-axis respectively, then what is the value of sin2a + sin2ß + sin2? . |
14.If | a + b |2 = | a |2 + | b | 2 , what is the angle between a and b ? |
15.If a is a unit vector and ( x - a ).( x + a ) = 8 , then find | x | |
16.If a unit vector a makes angles p with î , p with j and an acute angle ? with k , then 3 4 find ‘?’ |
17.Let a , b and c be the three vectors such that | a | = 3, | b | = 4, | c | = 5and each one of them being perpendicular to the sum of the other two, find |a + b+ c | |
18.If with reference to right handed system of mutually perpendicular unit vectors î, j and k, a = 3î – j, ß = 2î + j-3 k, then express ß in the form of ß = ß1 + ß2 where ß1 is parallel to a and ß2 is perpendicular to a |
19.Let a = î + 4j +2k , b = 3î - 2j + 7k and c = 2î – j + 4k . Find a vector d which is perpendicular to both a and b and c . d = 15 |
20.If a , b and c are the position vectors of the vertices A,B and C of a ?ABC. Show that the area of the ?ABC is 1 |a x b + b x c + c x a |. Also find the condition of the 2collinearity of these points. |
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22.If a , b and c are vectors such that a . b = a . c , a x b = a x c and |a | = 0 then prove that b = c |
23.Three vertices of a triangle are A(0,-1,-2) , B(3,1,4) and C(5,7,1). Show that it is a right angled triangle. Also find the other two angles |
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25.If a , b , and c are three mutually perpendicular vectors of equal magnitude, prove that a + b +c is equally inclined with vectors a , b and c |
PREPARED BY- RAJESH KUMAR GIRI
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Thanks for sharing the Basic Level & Introduction to Vectors with all of us as this is the very much important to know in Mathematics. Thank you once again
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