Chapter 6: Applications of Vector Algebra - Online Test
Q1. 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,
as coterminous edges is 8 cubic units, then the volume of the
parallelepiped with and as coterminous edges is,
Answer : Option C
Explaination / Solution:
No Explaination.
Q2. 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
, , , 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
Answer : Option A
Explaination / Solution:
No Explaination.
Q3. If 
, where , , are any three vectors such that . ≠ 0 and . ≠ 0 ,then and are
, where , , are any three vectors such that . ≠ 0 and . ≠ 0 ,then and are
Answer : Option B
Explaination / Solution:
No Explaination.
Q4. If 
then a vector
perpendicular to and lies in the plane containing and is
then a vector
perpendicular to and lies in the plane containing and is
Answer : Option D
Explaination / Solution:
No Explaination.
Q5. The angle between the lines 
and 
is
and is
Answer : Option D
Explaination / Solution:
No Explaination.
Q6. If the line 
lies in the plane x + 3y - α
z + β = 0, then (α , β ) is
lies in the plane x + 3y - α
z + β = 0, then (α , β ) is
Answer : Option B
Explaination / Solution:
No Explaination.
Q7. 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
= (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
Answer : Option C
Explaination / Solution:
No Explaination.
Q8. 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
= (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
Answer : Option D
Explaination / Solution:
No Explaination.
Q9. Distance from the origin to the plane 3x - 6 y +
2z + 7 = 0 is
Answer : Option B
Explaination / Solution:
No Explaination.
Q10. The distance between the planes x + 2 y + 3z + 7
= 0 and 2x + 4 y + 6z + 7 = 0 is
Answer : Option A
Explaination / Solution:
No Explaination.
