Question

Show that the dot product and cross product both satisfy the
product rule of differentiation of vectors.

Answer #1

Proof a•(b•c)=(a dot c)b-(a dot b)c
•=cross product
dot=dot product

What is the effect on the dot product of two vectors, if the
angle between the two vectors is fixed, but one of the vectors
doubles in length? or triples in length?
two explainations please

If A * B = 0 (the dot product), can you conclude that one of the
vectors has zero magnitude? Explain

2. Use the product rule for differentiation to find derivatives
in each of the following:
(a) ?(?)=(?2−4?−2)(?3+3?2−1)
(b) ?(?)=(2?2−1)(√?+2)
(c) ?(?)=(2/?2−3/?+2?)(3?−1)

1. Use the product rule for differentiation to find derivatives
in each of the following:
(a) ?(?)=(2?3+4?2−1)(3?2−5?−2)
(b) ?(?)=(2?4+1)(3√?−2)
(c) ?(?)=(3?−1)(6/?+4?−1)

True or False
A.The dot product of two vectors is always less than the
product of the lengths of the vectors.
B. All linear combinations of the vectors u= (u1,u2) and
v= (v1,v2) form the parallelogram whose adjacent sides are u and
v.
C. If A and B are square matrices of the same size, then
the second column of AB can be obtained by multiplying the second
column of A to the matrix B.
D. The vector that starts...

The cross product of 2 vectors, A and B, gives a
vector C that is perpendicular to the plane AB. But we can't always
contain two vectors in a plane (so we can't always find a plane AB) right?
Would the cross product be valid in this case? What would be the
result of the cross product?
Thanks in advance

Assuming two vectors are both located somewhere on the
xy-plane, how could you use the right-hand rule to
determine whether their cross product would point in the positive
z-direction (above the plane) or the negative
z-direction (below the plane)? Do not make reference to
which quadrant these vectors are in, since they could be in the
same quadrant or each could be in any quadrant. Consider instead
the order of the vectors in the cross product.

how do you find the cross product of vectors ?

How do economies of scale and product differentiation (both
desirable qualities) alter the nature of markets in the real world
in negative ways?

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