QJEEM21Ma128f: JEE Main 2021 Physics - Class 11 JEEM21Ma128f Solution: Let a → = i ^ + 5 j ^ + α k ^ , b → = i ^ + 3 j ^ + β k ^ and c …

Question

Verified Solution • 2025–26 Session moderate

Let

\vec{a} = \hat{i} + 5 \hat{j} + α \hat{k}

,

\vec{b} = \hat{i} + 3 \hat{j} + β \hat{k}

and

\vec{c} = - \hat{i} + 2 \hat{j} - 3 \hat{k}

be three vectors such that,

| \vec{b} \times \vec{c} | = 5 \sqrt{3}

and

\vec{a}

is perpendicular to

\vec{b}

. Then the greatest amongst the values of

{| \vec{a} |}^{2}

is _____________.

Accepted Answer

Since,

\vec{a} . \vec{b} = 0

1 + 15 + α β = 0 \Rightarrow α β = - 16

.... (1)

Also,

{| \vec{b} \times \vec{c} |}^{2} = 75 \Rightarrow (10 + β^{2}) 14 - (5 - 3 β)^{2} = 75

\Rightarrow

5

β

² + 30

β

+ 40 = 0

\Rightarrow

β

=

-

4,

-

2

\Rightarrow

α

= 4, 8

\Rightarrow {| \vec{a} |}_{max}^{2} = (26 + α^{2})_{max} = 90

Step-by-Step Verified Solution