{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

blueexam1sol.07f

# blueexam1sol.07f - blue MATH 32A Exam 1 LAST NAME FIRST...

This preview shows pages 1–4. Sign up to view the full content.

blue MATH 32A Exam 1 October 23, 2007 LAST NAME FIRST NAME ID NO. Your TA: To receive credit, you must write your answer in the space provided . DO NOT WRITE BELOW THIS LINE 1 (40 pts) 6 (20 pts) 2 (10 pts) 7 (20 pts) 3 (20 pts) 8 (30 pts) 4 (20 pts) 9 (20 pts) 5 (20 pts) TOTAL

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

View Full Document
2 PROBLEM 1 (40 Points) Let v = ( 1 , 2 , 1 ) , w = ( 1 , 1 , 1 ) Let θ be the angle between v and w . Calculate the quantities (A)-(D). (A) v · w = . (B) cos θ = . (C) v × w = . (D) The volume of the parallelepiped spanned by the vec- tors k , v and w . Volume = Solution: v · w = 1(1) + 2( 1) + ( 1)(1) = 2 . cos θ = v · w || v || · || w || = 2 radicalbig 1 + 2 2 + ( 1) 2 radicalbig 1 2 + ( 1) 2 + 1 2 = 2 6 3 = 2 3 2 = 2 3 v × w = vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle i j k 1 2 1 1 1 1 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = i 2 j 3 k = ( 1 , 2 , 3 ) Volume of the parallelepiped spanned by the vectors k , v and w is | k · ( v × w | = | − 3 | = 3
3 PROBLEM 2 (10 Points) Is the z -component of the cross product w × v positive or negative?

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 10

blueexam1sol.07f - blue MATH 32A Exam 1 LAST NAME FIRST...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online