# 17_new - HW06a – gilbert –(55035 1 This print-out...

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: HW06a – gilbert – (55035) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. Consequently, √ length = 38 . 1 10.0 points A rectangular box is constructed in 3- space with one corner at the origin and other ver-tices at (5, 0, 0), (0, 2, 0), (0, 0, 3) . Find the length of the diagonal of the box. 1. length = 17 length = √ 2. 33 3. length = 33 √ 4. length = 38 correct √ 5. length = 17 6. length = 38 keywords: length diagonal, rectangular solid, Pythagoras’ theorem, ThreeDimSys, 002 10.0 points Find an equation for the sphere centered at (3, 4, −2) that is tangent to the yz-coordinate plane. 1. x 2 + y 2 + z 2 − 6x − 8y + 4z + 25 = 2. x 2 + y 2 + z 2 + 6x + 8y − 4z + 25 = 3. x 2 + y 2 + z 2 − 6x − 8y + 4z + 20 = correct 4. x 2 + y 2 + z 2 − 6x − 8y + 4z + 13 = 5. x 2 + y 2 + z 2 + 6x + 8y − 4z + 13 = Explanation: We have to find the length of BD in the figure D G E F O C A B given that OA = 5 , OC = 2 , OD = 3 . Now by Pythagoras’ theorem, 6. x 2 + y 2 + z 2 + 6x + 8y − 4z + 20 = Explanation: Since the sphere touches the yz-plane, its radius, r, is the distance from its center, (3, 4, −2) to the yz-plane; thus r = 3. Con-sequently (x − 3) 2 + (y − 4) 2 + (z + 2) 2 = 9 is an equation for the sphere. After expansion this becomes x 2 + y 2 + z 2 − 6x − 8y + 4z + 20 = 0 . 003 10.0 points Find the trace on the xy-plane of the sphere having center at (1, 3, 1) and radius 3. length OB = length AC = √ 29 . 1. x 2 + y 2 − 2x − 6y + 2 = 0 correct But then, again by Pythagoras, 2. y 2 + z 2 − 6y − 2z + 2 = length BD = √ 38 ....
View Full Document

{[ snackBarMessage ]}

### Page1 / 6

17_new - HW06a – gilbert –(55035 1 This print-out...

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

View Full Document
Ask a homework question - tutors are online