JEE MATHS UNIT 12
QUIZ NO 1
TOTAL QUESTIONS = 20
1. If a vector has magnitude 5 and direction cosines l, m, n, then l^2 + m^2 + n^2 is equal to
A. 1
B. 5
C. 25
D. 0
2. The dot product of two perpendicular vectors is
A. 0
B. 1
C. -1
D. infinity
3. The cross product of two parallel vectors is
A. 0
B. 1
C. infinity
D. undefined
4. The magnitude of the vector 3i + 4j + 12k is
A. 13
B. 17
C. 12
D. 14
5. If a = 2i + 3j + k and b = i + 2j + 4k, then the dot product a·b is
A. 12
B. 11
C. 10
D. 9
6. The vector triple product of a, b, and c is expressed as
A. a × (b × c)
B. a · (b × c)
C. (a × b) × c
D. a + (b × c)
7. 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
8. The projection of vector a = 3i + 4j on vector b = i + j is
A. 7/sqrt(2)
B. 5/sqrt(2)
C. 1/sqrt(2)
D. 2/sqrt(2)
9. If vectors a = i + j + k and b = 2i + 3j + 4k, then a × b is
A. i - 2j + k
B. -i + 2j - k
C. i + 2j - k
D. -i - 2j + k
10. The area of a parallelogram with adjacent sides a = 2i + j and b = i - j is
A. sqrt(5)
B. sqrt(10)
C. 2sqrt(2)
D. 1
11. If vectors a = 3i - j and b = 2i + k are given, then a × b is
A. j - 3k
B. 2j - 3k
C. j + 3k
D. -j + 3k
12. The angle between two vectors a and b with dot product a·b = 0 is
A. 0°
B. 45°
C. 90°
D. 180°
13. If a = 3i + 4j and b = 6i + 8j, then a and b are
A. parallel
B. perpendicular
C. unit vectors
D. collinear
14. The magnitude of the cross product of two vectors a and b is equal to
A. |a||b|sinθ
B. |a||b|cosθ
C. |a||b|tanθ
D. |a||b|cotθ
15. If a = i - j and b = i + j, then the unit vector perpendicular to both is
A. k
B. -k
C. i
D. j
16. The scalar projection of a = 2i + j on b = i + j is
A. 3/sqrt(2)
B. 2/sqrt(2)
C. 1/sqrt(2)
D. 4/sqrt(2)
17. The volume of the 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|
18. The value of a·(b × c) is called
A. scalar triple product
B. vector triple product
C. scalar projection
D. vector projection
19. The cross product of two vectors a and b is a vector
A. perpendicular to both a and b
B. parallel to a and b
C. collinear with a
D. collinear with b
20. If a = i + j + k and b = 2i - j + k, then |a × b| is
A. sqrt(12)
B. sqrt(10)
C. sqrt(14)
D. sqrt(15)
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