Q. 4
Show that the vectors 
are coplanar, when
i. 
and 
ii. 
and 
iii. 
and 
Answer :
i. 
and 
Given Vectors :
To Prove : Vectors 
are coplanar.
i.e. 
Formulae :
1) Scalar Triple Product:
If
Then,
2) Determinant :
Answer :
For given vectors,
= 1(3) + 2(-6) + 3(3)
= 3 – 12 +9
= 0
Hence, the vectors 
are coplanar.
Note : For coplanar vectors 
,
ii. 
and 
Given Vectors :
To Prove : Vectors 
are coplanar.
i.e. 
Formulae :
1) Scalar Triple Product:
If
Then,
2) Determinant :
Answer :
For given vectors,
= 1(4) – 3(6) + 1(14)
= 4 – 18 + 14
= 0
Hence, the vectors 
are coplanar.
Note : For coplanar vectors 
,
iii. 
and 
Given Vectors :
To Prove : Vectors 
are coplanar.
i.e. 
Formulae :
1) Scalar Triple Product:
If
Then,
2) Determinant :
Answer :
For given vectors,
= 2(2) + 1(16) + 2(-10)
= 4 + 16 -20
= 0
Hence, the vectors 
are coplanar.
Note : For coplanar vectors 
,
Rate this question :
Questions Based on 3D Geometry | Check Yourself40 mins
Questions Based on 3D Geometry26 mins
Lecture on Product of Determinants58 mins
DNA Fingerprinting42 mins
Meselson and Stahl experiment49 mins
NEET 2021 | Transcription - An important Topic62 mins
Microsporogenesis & Megasporogenesis49 mins
Interactive Quiz on Microbes in Human Welfare29 mins
Interactive Quiz on Molecular basis of Inheritance-0234 mins
Methods of contraception47 mins
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
