Question

A vector of magnitude 100 N is inclined at angle of 30° to another vector of magnitude 50 N . Calculate the magnitude for cross product and dot product of two vectors

Answer 1

Given :

▪ Manitude of vector A = 100N

▪ Magnitude of vector B = 50N

▪ Angle b/w A and B = 30°

To Find :

❄ Magnitude of dot product and cross product.

Formula :

⚽ Dot product of two vectors :

$\bigstar\:\underline{\boxed{\bf{\red{\vec{A}\:{\tiny{\bullet}}\:\vec{B}=|\vec{A}| |\vec{B}|\cos\theta=AB\cos\theta }}}}$

⚽ Cross product of two vectors :

$\bigstar\:\underline{\boxed{\bf{\blue{\vec{A}\times\vec{B}=AB\sin\theta\:\hat{n}}}}}$

✴ $\hat{n}$ = unit vector (perpendicular to the plane of vectors A and B)

Calculation :

☣ Dot product :

$\dashrightarrow\sf\:\vec{A}\:{\tiny{\bullet}}\:\vec{B}=AB\cos\theta\\ \\ \dashrightarrow\sf\:\vec{A}\:{\tiny{\bullet}}\:\vec{B}=(100)(50)\cos30\degree\\ \\ \dashrightarrow\sf\:\vec{A}\:{\tiny{\bullet}}\:\vec{B}=5000\times \dfrac{\sqrt{3}}{2}\\ \\ \dashrightarrow\underline{\boxed{\bf{\green{\vec{A}\:{\tiny{\bullet}}\:\vec{B}=2500\sqrt{3}\:N}}}}\:\orange{\bigstar}$

☣ Cross product :

$\implies\sf\:\vec{A}\times \vec{B}=AB\sin\theta\:\hat{n}\\ \\ \implies\sf\:\vec{A}\times \vec{B}=(100)(50)\sin30\degree\:\hat{n}\\ \\ \implies\sf\:\vec{A}\times\vec{B}=5000\times\dfrac{1}{2}\:\hat{n}\\ \\ \implies\underline{\boxed{\bf{\purple{\vec{A}\times\vec{B}=2500\:N\:\hat{n}}}}}\:\gray{\bigstar}$

Answer 2

Answer:

find the attachment

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