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what is diffarence between Dot and Crossproducts? and give equations for both Cross and Dotproducts

RAJAVAMSI , 9 Years ago

Grade 11

2 Answers

sri tanish

Last Activity: 9 Years ago

Vector multiplication is of two types – 1 } scalar multiplication{dot product } 2} vector multiplication – {cross product }

In Euclidean space, a Euclidean vector is a geometrical object that possesses both a magnitude and a direction. A vector can be pictured as an arrow. Its magnitude is its length, and its direction is the direction that the arrow points. The magnitude of a vector A is denoted by $\left\| \mathbf{A} \right\|$ . The dot product of two Euclidean vectors A and B is defined by^[2]^[3]

$\mathbf A \cdot \mathbf B = \left\| \mathbf A \right\| \, \left\| \mathbf B \right\| \cos \theta ,$

where θ is the angle between A and B. so basically dot product is a scalar . depending on cosine of angle b\w the vectors . dot product is commutative .

CROSS PRODUCT:-

The magnitude of the cross product can be interpreted as the positive area of the parallelogram having a and b as sides (see Figure 1):

$A = \left\| \mathbf{a} \times \mathbf{b} \right\| = \left\| \mathbf{a} \right\| \left\| \mathbf{b} \right\| \sin \theta. \,\!$

SO CROSS PRODUCT is a vector depending on sine of angle b\w the vectors . CROSS PRODUCT IS NOT COMMUTATIVE , RATHER IT IS ANTI COMMUTATIVE .

SHAIK HAFEEZUL KAREEM

Last Activity: 9 Years ago

Vector multiplication is of two types – 1 } scalar multiplication{dot product } 2} vector multiplication – {cross product }

In Euclidean space, a Euclidean vector is a geometrical object that possesses both a magnitude and a direction. A vector can be pictured as an arrow. Its magnitude is its length, and its direction is the direction that the arrow points. The magnitude of a vector A is denoted by $\left\| \mathbf{A} \right\|$ . The dot product of two Euclidean vectors A and B is defined by^[2]^[3]

$\mathbf A \cdot \mathbf B = \left\| \mathbf A \right\| \, \left\| \mathbf B \right\| \cos \theta ,$

where θ is the angle between A and B. so basically dot product is a scalar . depending on cosine of angle b\w the vectors . dot product is commutative .

CROSS PRODUCT:-

The magnitude of the cross product can be interpreted as the positive area of the parallelogram having a and b as sides (see Figure 1):

SO CROSS PRODUCT is a vector depending on sine of angle b\w the vectors . CROSS PRODUCT IS NOT COMMUTATIVE , RATHER IT IS ANTI COMMUTATIVE .

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