Let \hat{ı}, \hat{} and \hat{k} be the unit vectors along the three positive coordinate axes. Let \overrightarrow{a}=3 \hat{ı}+\hat{}-\hat{k} \overrightarrow{b}=\hat{ı}+b_2 \hat{}+b_3 \hat{k}, b_2, b_3 \in \mathbb{R} \overrightarrow{c}=c_1 \hat{ı}+c_2 \hat{}+c_3 \hat{k}, c_1, c_2, c_3 \in \mathbb{R} be three vectors such that b_2 b_3>0, \overrightarrow{a} \cdot \overrightarrow{b}=0 and (\table 0 , -c_3 , c_2 ; c_3 , 0 , -c_1 ; -c_2 , c_1 , 0 )(\table 1 ; b_2 ; b_3 )=(\table 3-c_1 ; 1-c_2 ; -1-c_3 ) Then, which of the following is/are TRUE? [JEE Adv 2022 P2]

\overrightarrow{a} \cdot \overrightarrow{c}=0

\overrightarrow{b} \cdot \overrightarrow{c}=0

|\overrightarrow{c}| \leq \sqrt{11}

Vector Algebra

Section: Mathematics

Question : 9 of 38

Marks: +1, -0

Let

∧



and

∧

be the unit vectors along the three positive coordinate axes. Let

→

∧



−

∧

→

∧

+b2

∧



+b3

∧

,‌‌b2,b3∈ℝ

→

=c1

∧

+c2

∧



+c3

∧

,‌‌c1,c2,c3∈ℝ
be three vectors such that b2b3>0,

→

⋅

→

=0 and
(

0	−c3	c2
c3	0	−c1
−c2	c1	0

)(

)=(

3−c1

1−c2

−1−c3

)
Then, which of the following is/are TRUE?

[JEE Adv 2022 P2]

→
a
⋅
→
c
=0
→
b
⋅
→
c
=0
|
→
b
|>√10
|
→
c
|≤√11

Validate

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