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Question 6 - Week 7 Practice | Prasnya
Q6
00:00
3 Aug 2025
Q6.
Let
u
=
(
−
1
,
2
,
−
3
)
u=(-1,2,-3)
u
=
(
−
1
,
2
,
−
3
)
be a vector from the inner product space
R
3
\mathbb{R}^3
R
3
with the usual inner product. Which options are true?
A
There exist infinitely many vectors
v
∈
R
3
v\in\mathbb{R}^3
v
∈
R
3
such that
∥
v
∥
=
∥
u
∥
\|v\|=\|u\|
∥
v
∥
=
∥
u
∥
.
B
The set of all vectors orthogonal to
u
u
u
will lie on a line passing through the origin.
C
There exist infinitely many vectors
v
∈
R
3
v\in\mathbb{R}^3
v
∈
R
3
such that
⟨
u
,
v
⟩
=
0
\langle u,v\rangle=0
⟨
u
,
v
⟩
=
0
.
D
The set of all vectors orthogonal to
u
u
u
will form a subspace of
R
3
\mathbb{R}^3
R
3
.
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Check
Details
Q6
00:00
3 Aug 2025
Q6.
Let
u
=
(
−
1
,
2
,
−
3
)
u=(-1,2,-3)
u
=
(
−
1
,
2
,
−
3
)
be a vector from the inner product space
R
3
\mathbb{R}^3
R
3
with the usual inner product. Which options are true?
A
There exist infinitely many vectors
v
∈
R
3
v\in\mathbb{R}^3
v
∈
R
3
such that
∥
v
∥
=
∥
u
∥
\|v\|=\|u\|
∥
v
∥
=
∥
u
∥
.
B
The set of all vectors orthogonal to
u
u
u
will lie on a line passing through the origin.
C
There exist infinitely many vectors
v
∈
R
3
v\in\mathbb{R}^3
v
∈
R
3
such that
⟨
u
,
v
⟩
=
0
\langle u,v\rangle=0
⟨
u
,
v
⟩
=
0
.
D
The set of all vectors orthogonal to
u
u
u
will form a subspace of
R
3
\mathbb{R}^3
R
3
.
Save
Check
Details
