Question

Define scalar and vector product of two vectors

Answer 1

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The scalar or dot product of two vector can be defined as the product of magnitude of two vectors are the cosine of the angles between them. If a and b are the two vectors and thita is the angle between the two vectors.

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Answer 2

Answer:

Scalar product (Dot product) of two vectors is given by the expression:

$\vec A.\vec B=|\vec A|.|\vec B|.cos\theta$

Vector product (Cross product) of two vectors is given by the expression:

$\vec A\times\vec B=|\vec A |.|\vec B|.sin\theta$

Explanation:

The scalar product of any two given vectors, as the name suggests, gives us the result as a scalar quantity and only the magnitude of the product. It is found by the following simplified expression:

$\vec A.\vec B=|\vec A|.|\vec B|.cos\theta\\\vec A.\vec B=A_x.A_y+B_x.B_y+C_x.C_y$

It gives the result as a real number.

The vector product, as the name suggests, gives the product of two vectors in the form of another vector, i.e., it gives both the magnitude as well as the direction of the resultant vector.

It is generally found by the following simplified expression:

$\vec A\times\vec B=|\vec A |.|\vec B|.sin\theta\\\vec A\times\vec B=\hat i(A_yB_z-B_yA_z)-\hat j(A_xB_z-B_xA_z)+\hat k(A_xB_y-B_xA_y)$

Thus, the result is also in the form of $a_x\hat i+a_y\hat j+a_z\hat k$.