Question

Write pseudo - code that uses a function and array elements to find the vector dot product of two three dimensional vectors u and v . The vector dot product, in component form for sample vectors u and v , is defined as:

u dot v = u 1 v 1 + u 2 v 2 + u 3 v 3

Answer 1

To calculate the dot product of two three-dimensional vectors, a function checks if vectors are of the proper length, performs scalar multiplication of their respective components, sums these products, and returns the result as the scalar dot product.

Step-by-step explanation:

To find the dot product of two three-dimensional vectors u and v, we can use the following pseudo-code:

FUNCTION calculateDotProduct(u, v)
IF length(u) = 3 AND length(v) = 3 THEN
dotProduct = u[0] * v[0] + u[1] * v[1] + u[2] * v[2]
RETURN dotProduct
ELSE
RETURN 'Vectors must be three-dimensional'
END IF
END FUNCTION

In this pseudo-code, we define a function called calculateDotProduct which receives two arguments: arrays u and v. The function first checks if both vectors are of length 3, indicating that they are indeed three-dimensional.

If they are, the scalar multiplication of corresponding components is performed, and their sum represents the dot product. The result is then returned. If the vectors are not three-dimensional, an error message is returned.