Class 11 Exercise 3.2 Vectors NBF | XI Ex 3.2 NEW Maths book Federal Board National Book Foundation
Unit 1 Complex Number
Exercise 1.1
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Exercise 1.2
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Exercise 1.3
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Exercise 1.4
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Unit 2 Matrices and Determinate
Exercise 2.1
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Exercise 2.2
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Exercise 2.3
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Exercise 2.4
Exercise 2.5
Exercise 2.6
Unit 3 vectors
Exercise 3.1
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Exercise 3.2
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Exercise 3.3
Exercise 3.4
Unit 4 Sequence & Series
Exercise 4.1
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Exercise 4.2
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Exercise 4.3
Exercise 4.4
Exercise 4.5
Exercise 4.6
Unit 5 Polynomial
Exercise 5.1
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Exercise 5.2
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Exercise 5.3
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Class 11 vectors fbise
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1st year exercise 3.2 maths new book course
If a = 2î-3j+k; b = 1-3 + 4k and d = -î - 25 + 5k, then evaluate the followings.
(i) đ.b
(ii) 22. 36
(iii) (a - b).
(iv) (2a+36-2). (a + b)
(v) là + 3.b + k.č
2. If a = j-k; b = 31 - 43 + k and d = -1 + 29 - 4k, then find the angles between the vectors:
(i) a and 36
(ii) (2a-3b) and 22
(iii) (-a + c) and (b-2)
(iv) (a + b + c) and (a - b - c)
(v) (a-2b + c) and a
3. (i) If a, b and are three vectors such that vec a + vec b + vec c = 0 and [a] = 2; | | = 3 and [2]=4 then find angle between a and b.
(ii) If a + b = a - b, then find angle between a and b.
(i) If a = î-3j+4k; b = 7î-93 + k and d = 3î - 23+5k, find the value of a so that a - b is perpendicular to č.
(ii) Show that the angle between any two diagonals of a cube is arccos(1/3)
5. (i) If a = 21-39 + 4k, then find the direction cosine of
a- b along ĉ and projection of b along ĉ - a. Also find their vector projections. 6. (i) Three vertices of triangle are A(0, -1, -2); B(3, 1, 4) and C(5, 7, 1). Show that ABC is
a right-angled triangle and find the other two angles.
(ii) A vector is equally inclined with the coordinate axes and = 5. Find the vector 7.
7. (i) If a, b and ĉ are three vectors such that || = 2; 16 = 5; || = 4 and vec a + vec b + vec c = 0 then find the value of d. b + b. c + d. a
(ii) Show that angle in a semi-circle is a right angle.
11 . (i) Prove that altitudes of a triangle are concurrent.
(ii) Prove that angle bisectors of triangle are concurrent.
12. (i) Prove that cos(alpha + beta) = cos a * cos beta - sin a * sin beta
(ii) With usual notations for a triangle ABC; prove that c² = a² + b²-2abcos y and b = a cosy + c cos a
13. (i) The resultant of two vectors a and b is perpendicular to a and [a] == ||. Show that resultant of 7a and b is perpendicular to b.
(ii) Prove that a + b is equally inclined with a and b.
14. A force of F = 31-59 +7k newtons is applied on a body and moves it at a distance of 14 meters in the direction of the vector î-39+k. How much work is done?
15. Find the work done by the forces 21+39k and 3l + 7f + 4k acting on a particle in moving from point P to Q with position vectors î-39+k and 21-1+.
16. A box is dragged on the surface of a floor by a string that is applying a force of 30N at an angle of 30° with the floor. Find the work done by the force when the box is displaced up-to a distance of 10 meters.
