Q. 30
Mark (√) against the correct answer in the following:
If the volume of a parallelepiped having 
and 
as conterminous edges, is 216 cubic units then the value of λ is
A. 
B. 
C. 
D. 
Answer :
Given volume of the parallelepiped is 216 cubic units
Given 
And 
=
are the coterminous edges of the parallelepiped.
[
216
⇒216=
⇒ 216=5[21-(-2
]-(-4)[28-
]+1[-8-3]
⇒ 216=5[21+2
]+4[28-λ
]+1[-11]
⇒ 216= 105 +10 λ +112 -4 λ -11
⇒ 216-105-112+11=6 λ
⇒ 6 λ =10
⇒
=
⇒ λ = 
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The angle between two vectors 
and 
with magnitudes 
and 4, respectively, and 
is
True and False
If 
, then the vectors 
and 
are orthogonal.
Fill in the blanks
The vectors 
are the adjacent sides of a parallelogram. The acute angel between its diagonals is ____________.
Fill in the blanks
If 
is any non-zero vector, then 
equals ______.
True and False
If 
and 
are adjacent sides of a rhombus, then 
.
True and False
The formula 
is valid for non-zero vectors 
and 
.
Fill in the blanks
The vector 
bisects the angle between the non-collinear vectors 
and 
if ________
If 
and 
are two vectors such that 
then prove that vector 
is perpendicular to vector 
Mark the correct alternative in each of the following:
If θ is an acute angle and the vector 
is perpendicular to the vector 
then θ =
RD Sharma - Volume 2
Mark the correct alternative in each of the following:
is equal to
RD Sharma - Volume 2
