HSC Vectors Solved MCQ : Maharashtra Board

 

VECTORS

• This MCQs are based on the Mathematics Part I Textbook of Maharashtra (click here for reference).
• NCERT Vector Algebra.
• Click here for IIT JEE , CET and other Entrance Exams MCQ.
  

Q.1. If the vectors  are coplanar, then the value of a is_______.

(A) 3

(B) -3

(C) 2

(D) -2

Q.2. If , then the value of  for which  is perpendicular to  is

(A)

(B)

(C) 

(D) 

Q.3. Let  is a unit vector such that  equals

(A) 

(B)

(C) 

(D) 

Q.4. If  are the direction cosines of a line, then the value of  is

(A) 1

(B) 2

(C) 3

(D) 4

Q.5. If a line makes angles  with co-ordinate axis, then _______.

(A) 1

(B) -1

(C) 2

(D) -2

Q.6. If the vectors  are coplanar,, then the value of p is

(A) -2

(B) 1

(C) -1

(D) 2

Q.7. The volume of tetrahedron whose vertices are (1, -6, 10), (-1, -3, 7), (5, -1, ) and (7, -4, 7) is 11 cu. units, then the value of  is

(A) 7

(B) 

(C) 1

(D) 5

Q.8. If l, m, n are direction cosines of a line, then  is

(A) null vector

(B) the unit vector along the line

(C) any vector along the line

(D) a vector perpendicular to the line

Q.9. If then  lies in the interval

(A) 

(B) 

(C) 

(D) 

Q.10. The measure of acute angle between the lines whose direction ratios are 3, 2, 6 and -2, 1, 2 is _______.

(A) 

(B) 

(C) 

(D) 

Q.11. If  then  is equal to

(A) 24

(B) -24

(C) 0

(D) 48

Q.12. If sum of two unit vectors is itself a unit vector, then the magnitude of their difference is

(A) 

(B) 

(C) 1

(D) 2

Q.13. The line joining the points (-2, 1, -8) and (a, b, c) is parallel to the line whose direction ratios are 6, 2, 3. The values of a, b, c are

(A) 4, 3, -5

(B) 

(C) 10, 5, -2

(D) 3, 5, 11

Q.14. The value of  is 

(A) 0

(B) -1

(C) 1

(D) 3

Q.15. Let a, b, c be distinct non-negative numbers. If the vectors  and  lie in a plane, then c is

(A) the arithmetic mean of a and b

(B) the geometric mean of a and b

(C) the harmonic mean of a and b

(D) 0

Q.16. If  and  then the angle between  and  is

(A) 

(B) 

(C) 

(D) 

Q.17. If  are direction angles of a line and , then 

(A) 

(B) 

(C) 

(D) 

Q.18. The distance of the point (3, 4, 5) from Y-axis is

(A) 3

(B) 5

(C) 

(D) 

Q.19. Let  be distinct real numbers. The points with position vectors 

(A) are collinear

(B) form an equilateral triangle

(C) form a scalene triangle

(D) form a right angled triangle

Q.20. Let  be the position vectors of P and Q respectively, with respect to O and  The points R and S divide PQ internally and externally in the ratio 2 : 3 respectively. If OR and OS are perpendicular, then

(A) 

(B) 

(C) 9p = 4q

(D) 4p = 9q

Q.21. The 2 vectors  and and  represents the two sides AB and AC, respectively of a  The length of the median through A is

(A) 

(B) 

(C) 

(D) None of these

Q.22. If  are unit vectors, then what is the angle between  to be a unit vector?

(A) 

(B) 

(C) 

(D) 

Q.23. If  be the angle between any two vectors , then  when  is equal to

(A) 0

(B) 

(C) 

(D) 

Q.24. If the vectors  are collinear, then value of q is

(A) 5

(B) 10

(C) 

(D) 

Q.25. If  are non coplanar unit vectors such that  then the angle between  is 

(A) 

(B) 

(C) 

(D) 

Q.26. If a line is inclined at  and  with the X and Y-axis respectively, then the angle which it makes with Z-axis is

(A) 0

(B) 

(C) 

(D) 

Q.27. Which of the following represents direction cosines of the line?

(A) 

(B) 

(C) 

(D) 

Q.28. If  is equal to

(A) 0

(B) 1

(C) 2

(D) 3

Q.29. Direction cosines of the line passing through the points A(-4, 2, 3) and B(1, 3, -2) are

(A) 

(B) 

(C) 

(D)

Q.30. If the points A(2, 1, 1), B(0, -1, 4) and C(k, 3, -2) are collinear, then k=________.

(A) 0

(B) 1

(C) 4

(D) -4

Q.31. If ________.

(A) 100

(B) 101

(C) 110

(D) 109

Q.32. If a line makes angles  with the X, Y, Z axis respectively, then its direction cosines are_______.

(A) 

(B) 

(C) 

(D) 

Q.33. If  is_______.

(A) 100

(B) 110

(C) 109

(D) 10

Q.34. The direction ratios of the line which is perpendicular to the lines with direction ratios -1, 2, 2 and 0, 2, 1 are______.

(A) -2, -1, -2

(B) 2, 1, 2

(C) 2, -1, -2

(D) -2, 1, -2