If | \overrightarrow{a}\times \overrightarrow{b} | = \sqrt3 ...

CBSE Class 12 Math 2023 All Sets Solved Paper

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Question : 6 of 20

Marks: +1, -0

If

| {a}↖{→}× {b}↖{→} | = √3

and

{a}↖{→}.{b}↖{→} = -3,

then angle between

{a}↖{→}

and

{b}↖{→}

is

$\;{2π}/{3}$
${π}/{6}$
$\;{π}/{3}$
$\;{5π}/{6}$

Solution:

Given

|{a}↖{→} × {b}↖{→}|={√{3}}

and

{a}↖{→} ⋅ {b}↖{→}=-3

⇒|{a}↖{→}||{b}↖{→}||\sin θ|={√{3}} \text " and "|{a}↖{→}||{b}↖{→}| \cos θ=-3

Dividing both equations, we get

\tan θ=-\;{1}/{{√{3}}}

⇒ θ=\;{5 π}/{6}

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