Q. 55.0( 1 Vote )
Find the value of λ for which the vectors 
are coplanar, when
i. 
and 
ii. 
and 
iii. 
and 
Answer :
i. .
. and 
Given : Vectors 
are coplanar.
Where,
To Find : value of 
Formulae :
1) Scalar Triple Product:
If
Then,
2) Determinant :
Answer :
As vectors 
are coplanar
…………eq(1)
For given vectors,
…………eq(2)
From eq(1) and eq(2),
ii. 
and 
Given : Vectors 
are coplanar.
Where,
To Find : value of 
Formulae :
1) Scalar Triple Product:
If
Then,
2) Determinant :
Answer :
As vectors 
are coplanar
…………eq(1)
For given vectors,
…………eq(2)
From eq(1) and eq(2),
iii. .
. and 
Given : Vectors 
are coplanar.
Where,
To Find : value of 
Formulae :
1) Scalar Triple Product:
If
Then,
2) Determinant :
Answer :
As vectors 
are coplanar
…………eq(1)
For given vectors,
…………eq(2)
From eq(1) and eq(2),
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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
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