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,

$\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:.\:\vec{b}\:=\:ab\cos{\theta}\:}}}}$

Where,

• θ = 90°

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

• cos 90° = 0

$\rm{\implies\:\vec{a}\:.\:\vec{b}\:=\:ab\times{0}\:}$

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

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

✍️ We have know that,

$\orange\bigstar\:\rm{\pink{\boxed{\green{\vec{a}\:\times\:\vec{b}\:=\:ab\sin{\theta}\:}}}}$

Where,

• θ = 90°

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\sin{90^{\degree}}\:}$

• sin 90° = 1

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\times{1}\:}$

$\rm{\implies\:\vec{a}\:\times\:\vec{b}\:=\:ab\:}$

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