JEE MATHS UNIT 12
QUIZ NO 4
TOTAL QUESTIONS = 20
1. The magnitude of the vector 3i + 4j is
A. 5
B. 7
C. 6
D. 9
2. If a = 2i - j and b = i + j, then a · b is
A. 1
B. 2
C. 3
D. -1
3. The cross product of two parallel vectors is always
A. 0
B. 1
C. infinity
D. undefined
4. The magnitude of a unit vector is
A. 1
B. 0
C. infinity
D. undefined
5. The projection of a vector a = 3i + 4j on b = i + j is
A. 7/sqrt(2)
B. 5/sqrt(2)
C. 2/sqrt(2)
D. 3/sqrt(2)
6. If a = i + j + k and b = 2i - j + k, then the value of a × b is
A. -2i - 3j - k
B. -2i + 3j - k
C. 2i - 3j + k
D. -2i - 3j + k
7. The dot product of two vectors is equal to
A. |a||b|cosθ
B. |a||b|sinθ
C. |a||b|tanθ
D. |a||b|cotθ
8. The scalar triple product of a, b, and c is equal to
A. a · (b × c)
B. a × (b × c)
C. a + b + c
D. a · b + c
9. The area of a triangle formed by vectors a = 3i - j and b = i + j is
A. sqrt(5)/2
B. sqrt(10)/2
C. 2sqrt(2)/2
D. 1/2
10. The volume of a parallelepiped formed by vectors a, b, and c is given by
A. |a · (b × c)|
B. |a × b + c|
C. |a + b + c|
D. |a × b × c|
11. The magnitude of the cross product of vectors a = 3i + 4j and b = i - j is
A. 5
B. 7
C. sqrt(26)
D. sqrt(10)
12. If a = i + 2j and b = 3i + 4j, then a and b are
A. neither parallel nor perpendicular
B. parallel
C. perpendicular
D. unit vectors
13. The direction cosines of the vector i + j are
A. 1/sqrt(2), 1/sqrt(2), 0
B. 1/sqrt(3), 1/sqrt(3), 1/sqrt(3)
C. 0, 0, 1
D. 1, 0, 0
14. If the cross product of two vectors is zero, the vectors are
A. parallel
B. perpendicular
C. equal
D. collinear
15. The scalar projection of a vector a on b is given by
A. (a · b)/|b|
B. (a × b)/|b|
C. (a + b)/|b|
D. (a - b)/|b|
16. The angle between two vectors a and b is 90° if
A. a · b = 0
B. a × b = 0
C. |a| = |b|
D. a = b
17. If a = 2i + j + k and b = i - 2j + k, then the value of a × b is
A. 3i + 3j - 5k
B. -3i - 3j + 5k
C. 3i - 3j + 5k
D. -3i + 3j - 5k
18. The magnitude of vector a = 4i - 3j is
A. 5
B. 7
C. sqrt(25)
D. sqrt(50)
19. The dot product of two unit vectors is equal to
A. cosθ
B. sinθ
C. tanθ
D. cotθ
20. If a = i + 2j - k and b = 3i - j + k, then the angle between a and b is
A. cos^-1(1/sqrt(10))
B. sin^-1(1/sqrt(10))
C. tan^-1(1/sqrt(10))
D. cos^-1(2/sqrt(10))
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