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[tex]\sf{\pink{\underline{\underline{\blue{GIVEN:-}}}}}[/tex]

  • The angle between the two vectors is 90° .

[tex]\sf{\pink{\underline{\underline{\blue{TO\: FIND:-}}}}}[/tex]

  1. The dot product of two vectors .
  2. The cross product of two vectors .

[tex]\sf{\pink{\underline{\underline{\blue{SOLUTION:-}}}}}[/tex]

⚡ Let [tex]\rm{\vec{a}}[/tex] and [tex]\rm{\vec{b}}[/tex] are the two vectors .

✍️ We have know that,

[tex]\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:.\:\vec{b}\:=\:ab\cos{\theta}\:}}}}[/tex]

Where,

  • θ = 90°

[tex]\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\cos{90^{\degree}}\:}[/tex]

  • cos 90° = 0

[tex]\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\times{0}\:}[/tex]

[tex]\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:0\:}[/tex]

[tex]\rm{\red{\therefore}}[/tex] [1] The dot product of two vectors is “ 0 ” .

✍️ We have know that,

[tex]\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:\times\:\vec{b}\:=\:ab\sin{\theta}\:}}}}[/tex]

Where,

  • θ = 90°

[tex]\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\sin{90^{\degree}}\:}[/tex]

  • sin 90° = 1

[tex]\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\times{1}\:}[/tex]

[tex]\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\:}[/tex]

[tex]\rm{\red{\therefore}}[/tex] [2] The cross product of two vectors is “ ab ” .

the dot and cross product will become zero if the angle becomes 90°

hope it helps you...

#from india ✌✌✌

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