Question

what is the dot product of two similar unit vectors

Answer 1

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The dot product of two unit vectors is cosine of angle between the vectors.

This can be explained as follows:

Let the unit vector be a1 and other be b1
now the magnitude of both is 1 since they are unit vector.

Let the angle between them be@

So by the formula,
a1.b1 = abcos@
= 1.1.cos@
= cos@


Now if the unit vectors are along same direction then @=0°
i.e. cos 0=1

So their dot product will be 1 when they are along same direction and if not then their dot product is equal to cosine of the angle between them.



HOPE THIS HELPS YOU:)


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Answer 2

Answer:

The dot product of two vectors is commutative, which means that the order of the vectors in the product makes no difference. Multiplying a vector by a constant multiplies its dot product with any other vector by the same constant.

Explanation:

The dot product, also known as the inner product, of two vectors is the sum of the products of their corresponding components. It is the product of their magnitudes multiplied by the cosine of the angle between them. A vector's dot product with itself is the square of its magnitude. Two unit vectors' dot product is always one. The sum of two unit vectors is always greater than the difference of their magnitudes.