If a - and b - are two vectors of the same magnitude inclined at an angle of 60- such that a - - b -8- write the value of their magnitude-

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Standard XII

Mathematics

Angle of Intersection of Two Curves

If a → and b ...

Question

If $\vec{a} and \vec{b}$ are two vectors of the same magnitude inclined at an angle of 60° such that $\vec{a} . \vec{b} = 8,$ write the value of their magnitude.

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Solution

$Given that |\vec{a}| = |\vec{b}| and \vec{a} and \vec{b} are inclined at an angle of 60 ° Also, given that \vec{a} . \vec{b} = 8 \Rightarrow |\vec{a}| |\vec{b}| \cos 60 ° = 8 \Rightarrow |\vec{a}| |\vec{a}| (\frac{1}{2}) = 8 \Rightarrow {|\vec{a}|}^{2} = 16 \Rightarrow |\vec{a}| = 4$

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If a →and b →are two vectors of the same magnitude inclined at an angle of 60° such that a →.b →=8, write the value of their magnitude.

Given thata→=b→ and a→ and b→ are inclined at an angle of 60°Also, given thata→. b→=8⇒a→ b→ cos 60°=8⇒a→a→ 12=8⇒a→2=16⇒a→=4

If $\vec{a} and \vec{b}$ are two vectors of the same magnitude inclined at an angle of 60° such that $\vec{a} . \vec{b} = 8,$ write the value of their magnitude.

$Given that |\vec{a}| = |\vec{b}| and \vec{a} and \vec{b} are inclined at an angle of 60 ° Also, given that \vec{a} . \vec{b} = 8 \Rightarrow |\vec{a}| |\vec{b}| \cos 60 ° = 8 \Rightarrow |\vec{a}| |\vec{a}| (\frac{1}{2}) = 8 \Rightarrow {|\vec{a}|}^{2} = 16 \Rightarrow |\vec{a}| = 4$