problem_set_5

problem_set_5 - Name Section Student ID Last First MI Math...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Name: First MI Last Student ID # Problem Set #5 Score Section: C REDIT 2 1 0 Problem #1 . Let I and J denote any two orthogonal unit vectors in R 3 which both happen to have a z –com- ponent of zero. Find, to within a sign, the value of I × J – and show all of your reasoning. Math 32A Lecture #5 Fall 2007 C REDIT 2 1 0 Problem #2 . Let A ( t ) and B ( t ) denote two vector valued functions of time. Derive a formula for the deriva- tive of the cross product: d dt A × B . Hint: You can try a derivation on the (primitive) de± nition which involves the basis vectors.
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2 Problem Set #5 C REDIT 2 1 0 Problem #4 . Let r A and r B denote (non–zero) vectors in R n . Although these have a dot product, you may not assume anything like the formula involving dot products and cosines of angles. In fact, something like this is what we will show in the form of an inequality. Part I. Show that for any scalar λ , | r A | 2 + λ 2 | r B | 2 2 λ r A r B . Part II. Find the optimal constant λ which makes the left and right side of the above inequality as close as pos- sible. Plugging in that value of λ , obtain a famous inequality involving | r A |, | r B | and r A r B . C
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 6

problem_set_5 - Name Section Student ID Last First MI Math...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online