Topic: Chapter 6: Applications of Vector Algebra (Test 2)



Topic: Chapter 6: Applications of Vector Algebra
Q.1
If the volume of the parallelepiped with  as coterminous edges is 8 cubic units, then the volume of the parallelepiped with  and  as coterminous edges is,
A. 8 cubic units
B. 512 cubic units
C. 64 cubic units
D. 24 cubic units
Answer : Option C
Explaination / Solution:
No Explaination.


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Q.2
Consider the vectors   such that  . Let P1 and P2 be the planes determined by the pairs of vectors and    respectively. Then the angle between P1 and P2 is
A.
B. 45˚
C. 60˚
D. 90˚
Answer : Option A
Explaination / Solution:
No Explaination.


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Q.3
If , where  are any three vectors such that    0 and    0 ,then  and  are
A. perpendicular
B. parallel
C. inclined at an angle π/3
D. inclined at an angle π/3
Answer : Option B
Explaination / Solution:
No Explaination.


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Q.4
If  then a vector perpendicular to  and lies in the plane containing  and  is
A. -17iˆ + 21 ˆj - 97kˆ
B. 17iˆ + 21 ˆj -123kˆ
C. -17iˆ - 21 ˆj + 97kˆ
D. -17iˆ - 21 ˆj - 97kˆ
Answer : Option D
Explaination / Solution:
No Explaination.


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Q.5
The angle between the lines  and  is
A. π/6
B. π/4
C. π/3
D. π/2
Answer : Option D
Explaination / Solution:
No Explaination.


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Q.6
If the line  lies in the plane x + 3y - α z + β = 0, then (α , β ) is
A. (-5, 5)
B. (-6, 7)
C. (5, -5)
D. (6, -7)
Answer : Option B
Explaination / Solution:
No Explaination.


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Q.7
The angle between the line  = (ˆ i + 2 ˆ j - 3 ˆ k ) + t(2 ˆ i + ˆ j - 2 ˆ k ) and the plane  = (ˆ i + ˆ j) + 4 = 0 is
A.
B. 30˚
C. 45˚
D. 90˚
Answer : Option C
Explaination / Solution:
No Explaination.


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Q.8
The coordinates of the point where the line  = (6 ˆ i - ˆ j - 3 ˆ k ) + t(-ˆ i + 4 ˆ k ) meets the plane .( ˆ i + ˆ j - ˆ k ) = 3 are
A. (2,1, 0)
B. (7, -1, -7)
C. (1, 2, -6)
D. (5, -1,1)
Answer : Option D
Explaination / Solution:
No Explaination.


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Q.9
Distance from the origin to the plane 3x - 6 y + 2z + 7 = 0 is
A. 0
B. 1
C. 2
D. 3
Answer : Option B
Explaination / Solution:
No Explaination.


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Q.10
The distance between the planes x + 2 y + 3z + 7 = 0 and 2x + 4 y + 6z + 7 = 0 is
A. √7 / 2√2
B. 7/2
C. √7 / 2
D. 7 / 2√2
Answer : Option A
Explaination / Solution:
No Explaination.


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