Question:
Consider the following statements with respect to a vector da bc () : I. d is coplanar with a and d II. d is perpendicular to c Oswaal NDA/NA Year-wise Solved Papers Which of the statements given above is/are correct?
Consider the following statements with respect to a vector da bc () : I. d is coplanar with a and d II. d is perpendicular to c Oswaal NDA/NA Year-wise Solved Papers Which of the statements given above is/are correct?
Options:
- a) I only
- b) II only
- c) Both I and II
- d) Neither I nor II
- a) I only
- b) II only
- c) Both I and II
- d) Neither I nor II
correct answer : c)
Explanation:
da bc
=× ×() = (. )( .)ac bb ca
– …(i)
Since d
is a linear combination of a
and b
.
Therefore d
lies in the plane formed by a
and
b
.
So, d
is coplanar with a
and b
.
dc
. = ac bb ca c
.. .() – ()
= ac bc bc ac
.. ..() () – () () = 0
So, d
is perpendicular to c
Hence both statements are true.
da bc
=× ×() = (. )( .)ac bb ca
– …(i)
Since d
is a linear combination of a
and b
.
Therefore d
lies in the plane formed by a
and
b
.
So, d
is coplanar with a
and b
.
dc
. = ac bb ca c
.. .() – ()
= ac bc bc ac
.. ..() () – () () = 0
So, d
is perpendicular to c
Hence both statements are true.