yellowexam1sol.08w

yellowexam1sol.08w - blue MATH 32A Exam 1 LAST NAME FIRST...

This preview shows pages 1–5. Sign up to view the full content.

blue MATH 32A Exam 1 January 30, 2008 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 (20 pts) 5 (20 pts) 2 (10 pts) 6 (20 pts) 3 (20 pts) 7 (20 pts) 4 (20 pts) TOTAL

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

View Full Document
2 PROBLEM 1 (20 Points) Find the cosine of the angle between the two planes with equations 2 x + 2 y - z = 4 , - x - y + 3 z = 12 Answer : Solution: By deﬁnition, the angle θ between two planes is equal to the angle between their normal vectors. In our case, the normal vectors are n 1 = h 2 , 2 , - 1 i , n 2 = h- 1 , - 1 , 3 i and cos θ = n 1 · n 2 || n 1 |||| n 2 || = 2( - 1) + 2( - 1) - 1(3) 9 · 11 = - 7 3 11
3 PROBLEM 2 (20 Points) (A) Determine || v - 3 w || where the angle between v and w is θ = π 4 and their lengths are || v || = 2 , || w || = 5 Answer : (B) Find cos θ where θ is the angle between vectors v and w such that || v || = 4 , || w || = 2 , || v + w || = 3 Answer :

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

View Full Document
4 Solution: (A) We have || v - 3 w || 2 = ( v
This is the end of the preview. Sign up to access the rest of the document.

This test prep was uploaded on 04/22/2008 for the course MATH 32A taught by Professor Gangliu during the Winter '08 term at UCLA.

Page1 / 11

yellowexam1sol.08w - blue MATH 32A Exam 1 LAST NAME FIRST...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online