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DAILY PRACTICE PAPERS CHAPTERWISE & TOPICWISE DPP  EACH QUESTION WITH DETAILED SOLUTION BEST FOR JEE MAIN / NEET & BOARDS QUESTIONS ARRANGED LEVELWISE  AVAILABLE IN Ms WORD & PDF ☎ LATEST LAUNCHED AVAILABLE CHAPTERWISE-TOPICWISE FEATURE S 2000/- PER SUBJECT
MATHEMATICS DPP DAILY PRACTICE PAPER VECTOR ALGEBRA DPP No. 19 Modulus of vector, Algebra of vectors 1. The perimeter of a triangle with sides 3i + 4j + 5k, 4i − 3j − 5k and 7i + j is (a) 450 (b) 150 (c) 50 (d) 200 2. If the position vectors of the vertices of a triangle be 2i + 4j − k, 4i + 5j + k and 3i + 6j − 3k, then the triangle is (a) Right angled (b) Isosceles (c) Equilateral (d) Right angled isosceles 3. If one side of a square be represented by the vector 3i + 4j + 5k, then the area of the square is (a) 12 (b) 13 (c) 25 (d) 50 4. If a = 2i + 2j − k and |x a| = 1, then x = (a) 3 1  (b) 4 1  (c) 5 1  (d) 6 1  5. Which of the following is not a unit vector for all values of  (a) (cos)i −(sin)j (b) (sin)i +(cos)j (c) (sin 2)i −(cos)j (d) (cos 2)i − (sin 2)j 6. If a + b bisects the angle between a and b, then a and b are (a) Mutually perpendicular (b) Unlike vectors (c) Equal in magnitude (d) None of these 7. If a = i + 2j + 2k and b = 3i + 6j + 2k, then a vector in the direction of a and having magnitude as |b| is (a) 7(i + j + k) (b) ( 2 2 ) 3 7 i + j + k (c) ( 2 2 ) 9 7 i + j + k (d) None of these 8. If p = 7i − 2j + 3k and q = 3i + j + 5k, then the magnitude of p − 2q is (a) 29 (b) 4 (c) 62 − 2 35 (d) 66 9. Let a = i be a vector which makes an angle of o 120 with a unit vector b. Then the unit vector (a + b) is (a) i j 2 3 2 1 − + (b) i j 2 1 2 3 − + (c) i j 2 3 2 1 + (d) i j 2 1 2 3 −
MATHEMATICS DPP DAILY PRACTICE PAPER VECTOR ALGEBRA DPP No. 19 10. If the position vectors of the vertices of a triangle be 6i + 4j + 5k, 4i + 5j + 6k and 5i + 6j + 4k, then the triangle is (a) Right angled (b) Isosceles (c) Equilateral (d) None of these 11. The perimeter of the triangle whose vertices have the position vectors (i + j + k), (5i + 3j − 3k) and (2i + 5j + 9k), is given by (a) 15 + 157 (b) 15 − 157 (c) 15 − 157 (d) 15 + 157 12. The position vectors of two points A and B are i + j − k and 2i − j + k respectively. Then | AB| = (a) 2 (b) 3 (c) 4 (d) 5 13. The magnitudes of mutually perpendicular forces a, b and c are 2, 10 and 11 respectively. Then the magnitude of its resultant is (a) 12 (b) 15 (c) 9 (d) None 14. The system of vectors i, j, k is (a) Orthogonal (b) Coplanar (c) Collinear (d) None of these 15. The direction cosines of the resultant of the vectors (i + j + k), (−i + j + k), (i − j + k) and (i + j − k), are (a)         6 1 , 3 1 , 2 1 (b)         6 1 , 6 1 , 6 1 (c)         − − − 6 1 , 6 1 , 6 1 (d)         3 1 , 3 1 , 3 1 16. The position vectors of P and Q are 5i + 4j + ak and −i + 2j − 2k respectively. If the distance between them is 7, then the value of a will be (a) – 5, 1 (b) 5, 1 (c) 0, 5 (d) 1, 0 17. A zero vector has (a) Any direction (b) No direction (c) Many directions (d) None of these 18. A unit vector a makes an angle 4  with z-axis. If a + i + j is a unit vector, then a is equal to (a) 2 2 2 i j k + + (b) 2 2 2 i j k + − (c) 2 2 2 i j k − − + (d) None of these
MATHEMATICS DPP DAILY PRACTICE PAPER VECTOR ALGEBRA DPP No. 19 19. A force is a (a) Unit vector (b) Localised vector (c) Zero vector (d) Free vector 20. If a, b, c, d be the position vectors of the points A, B, C and D respectively referred to same origin O such that no three of these points are collinear and a + c = b + d, then quadrilateral ABCD is a (a) Square (b) Rhombus (c) Rectangle (d) Parallelogram 21. If the position vectors of A and B are i + 3j − 7k and 5i − 2j + 4k, then the direction cosine of AB along y-axis is (a) 162 4 (b) 162 5 − (c) – 5 (d) 11 22. If the resultant of two forces is of magnitude P and equal to one of them and perpendicular to it, then the other force is (a) P 2 (b) P (c) P 3 (d) None of these 23. The direction cosines of vector a = 3i + 4j + 5k in the direction of positive axis of x, is (a) 50 3  (b) 50 4 (c) 50 3 (d) 50 4 − 24. The point having position vectors 2i + 3j + 4k, 3i + 4j + 2k, 4i + 2j + 3k are the vertices of (a) Right angled triangle (b)Isosceles triangle (c) Equilateral triangle (d) Collinear 25. Let , ,  be distinct real numbers. The points with position vectors i + j + k, i + j +k, i +j + k (a) Are collinear (b) Form an equilateral triangle (c) Form a scalene triangle (d) Form a right angled triangle 26. If |a | = 3, |b | = 4 and |a + b | = 5, then |a − b| = (a) 6 (b) 5 (c) 4 (d) 3 27. If OP = 8 and OP makes angles o 45 and o 60 with OX-axis and OY-axis respectively, then OP = (a) 8( 2i + j  k) (b) 4 ( 2i + j  k) (c) ( 2 ) 4 1 i + j  k (d) ( 2 ) 8 1 i + j  k