JEE MATHS UNIT 12
QUIZ NO 2
TOTAL QUESTIONS = 20
1. The magnitude of the vector 4i + 3j + 12k is
A. 13
B. 14
C. 17
D. 12
2. The dot product of two vectors a = 2i + j and b = 4i - j is
A. 7
B. 9
C. 8
D. 10
3. If a and b are two vectors and a × b = 0, then the vectors are
A. parallel
B. perpendicular
C. equal
D. collinear
4. 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
5. The scalar triple product of three vectors a, b, and c is represented as
A. a · (b × c)
B. a × (b × c)
C. a · b · c
D. (a + b + c)
6. The cross product of a = i + 2j - k and b = 2i - j + 3k is
A. (7i + j + 5k)
B. (i - j + k)
C. (7i + j - 5k)
D. (-7i - j - 5k)
7. If a = 3i + j + 2k and b = i - j + 4k, the value of |a × b| is
A. sqrt(29)
B. sqrt(35)
C. sqrt(49)
D. sqrt(45)
8. The area of a triangle formed by vectors a = 2i + j and b = i - j is
A. sqrt(5)/2
B. sqrt(10)/2
C. 2sqrt(2)/2
D. 1/2
9. If vectors a = 2i + j and b = i - 3j, then a · b is
A. -1
B. 5
C. 2
D. -5
10. The direction cosines of a vector 2i + 2j + 1k are
A. 2/sqrt(9), 2/sqrt(9), 1/sqrt(9)
B. 1/3, 1/3, 1/3
C. 2/3, 2/3, 1/3
D. 1/2, 1/2, 1/3
11. If the magnitude of a vector is 1, it is called a
A. unit vector
B. null vector
C. position vector
D. scalar vector
12. The value of (i + j + k) × (i - j - k) is
A. 2j - 2k
B. 2i + 2j
C. 0
D. 2i - 2k
13. The magnitude of the projection of 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)
14. If a and b are vectors such that a × b = 0 and a ≠ 0, b ≠ 0, then
A. a and b are parallel
B. a and b are perpendicular
C. a and b are collinear
D. a and b are unit vectors
15. 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|
16. If a = i + 2j - k and b = -i + 3j + k, then the angle between a and b is given by
A. cos^-1(2/sqrt(15))
B. sin^-1(2/sqrt(15))
C. tan^-1(2/sqrt(15))
D. cos^-1(1/sqrt(15))
17. The vector projection of a on b is given by
A. (a · b)b/|b|^2
B. (a × b)b/|b|^2
C. (a + b)b/|b|^2
D. (a · b)b/|b|
18. If a = i + j + k and b = 2i - j + 3k, then a × b is
A. 4i - k + 5j
B. -4i + k - 5j
C. 4i + k - 5j
D. -4i - k + 5j
19. If the magnitude of vector a = 2i - 3j + k is 14, then k is
A. 13
B. 11
C. 12
D. sqrt(11)
20. The value of a·(b × c) is always
A. scalar
B. vector
C. both scalar and vector
D. neither scalar nor vector
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