samsoln23x1s10

# samsoln23x1s10 - MATH 23 Sample First Exam was February...

This preview shows pages 1–2. Sign up to view the full content.

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.

Unformatted text preview: MATH 23 Sample First Exam was: February, 2003 NAME : Dodson, B. Section 110-313 (Last, First) 1. (15 points ) If U, V and W are the vectors U = i- 3 j + k, V = 2 i- j + 3 k and W =- i + 2 j- k, where i, j and k are the unit vectors in the direction of the coordinate axes, find the following. (a) the dot product of U and V U · V = 2 + 3 + 3 = 8 . (b) the scalar projection of V onto W (= component of V in the direction of W ) comp W ( V ) = V · W | W | =- 2- 2- 3 √ 1+4+1 =- 7 √ 6 . (c) the vector projection of V onto W proj W ( V ) = comp W ( V ) u W =- 7 √ 6 1 √ 6 ‡- i + 2 j- k · =- 7 6 ‡- i + 2 j- k · , where u W is the unit vector in the direction of W . 2. (10 points ) Find the center and radius of the sphere with equation x 2- 6 x + y 2 + 2 y + z 2 = 3 . x 2- 6 x + 9 + y 2 + 2 y + 1 + z 2 = 3 + 9 + 1 , so ( x- 3) 2 + ( y + 1) 2 + z 2 = 13 , and center = (3, -1, 0), radius = √ 13 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

samsoln23x1s10 - MATH 23 Sample First Exam was February...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online