Question

what is the dot product and cross product of of two vectors if the angle is between them is 90 degree?​

Answer 1

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

hope it helps you...

#from india ✌✌✌

Answer 2

`\sf{\pink{\underline{\underline{\blue{GIVEN:-}}}}}`

• The angle between the two vectors is 90° .

`\sf{\pink{\underline{\underline{\blue{TO\: FIND:-}}}}}`

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

`\sf{\pink{\underline{\underline{\blue{SOLUTION:-}}}}}`

⚡ Let
`\rm{\vec{a}}` and
`\rm{\vec{b}}` are the two vectors .

✍️ We have know that,

`\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:.\:\vec{b}\:=\:abcos(\theta)\:}}}}`

Where,

• θ = 90°

`\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\cos{90^(\degree)}\:}`

• cos 90° = 0

`\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab*{0}\:}`

`\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:0\:}`

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

✍️ We have know that,

`\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:*\:\vec{b}\:=\:absin(\theta)\:}}}}`

Where,

• θ = 90°

`\rm{\implies\:\vec{a}\:*\:\vec{b}\:=\:ab\sin{90^(\degree)}\:}`

• sin 90° = 1

`\rm{\implies\:\vec{a}\:*\:\vec{b}\:=\:ab*{1}\:}`

`\rm{\implies\:\vec{a}\:*\:\vec{b}\:=\:ab\:}`

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