1. 2. 3. 4. 5. Find the center and radius of the sphere. (x + 7)2 + y2 + (z - 7)
ID: 3343847 • Letter: 1
Question
1.
2.
3.
4.
5.
Find the center and radius of the sphere. (x + 7)2 + y2 + (z - 7)2 = 27 The center of the sphere is . (Type an ordered triple.) The radius of the sphere is . (Type an exact answer, using radicals as needed.) Express the vector 8i - 14j - 8k as a product of its length and direction. 8i - i4j - 8k = [( )i + ( )j + ( )k] (Simplify your answers. Use integers or fractions for any numbers in the expression.) Given the vectors v and u, answer a. through d. below. v = 4i - 2k u = i + j + k Find the dot product of v and u. u v = Find the length of v. |v| = (Type an exact answer, using radicals as needed.) Find the length of u. |u| = (Type an exact answer, using radicals as needed.) Find the cosine of the angle between v and u. cos theta = (Type an exact answer, using radicals as needed.) Find the scalar component of u in the direction of v. (Type an exact answer, using radicals as needed.) Find the vector projection of u onto v. = (Type your answer in terms of i, j, and k.) Describe the given set with a single equation or with a pair of equations. The circle of radius 3 centered at (0, 3, 0) and lying in a. the xy-plane b. the yz-plane c. the plane y = 3 Choose the correct set of points lying in the xy-plane. x2 + y2 = 9, z = 0 (x-3)2 + y2 = 9, z = 0 x2 + y2 + z2 = 9, z = 0 x2 + (y-3)2 = 9, z = 0 Choose the correct set of points lying in the yz-plane. y2 + (z - 3)2 = 9, x = 0 x2 + y2 + z2 = 9, x = 0 (y - 3)2 + z2 = 9, x = 0 y2 + z2 = 9, x = 0 Choose the correct set of points lying in the plane y = 3. x2 + y2 + z2 = 9, y = 3 x2 + z2 = 9, y = 3 (x - 3)2 + z2 = 9, y = 0 x2 + (z - 3)2 = 9, y = 0 Find the distance between points Pt and P2. P1(2,4,3), P2 (2,0,6) The distance is .Explanation / Answer
radius : square root(27) = 3*root(3) = 5.19
2) 8i - 14j - 8k
length =sqrt(64 +196 +64)
= 18
so ans will be
18*(0.44i - 0.77j - 0.44k)
3) u.v = (4*1) +(-2*1)+(0*1)
= 4 -2 +0 = 2
|V| = sqrt( 16 +4) = sqrt(20)
|u| = sqrt(1+1+1) = sqrt 3
cos(theta) = |U.V|/[ |U||V|]
= 2/[ sqrt20 * sqrt3]
=> theta= 75 degrees
5) P1= ( 2,4,3), P2 = (2,0,6)
distance = sqrt [ ( 2-2)^2 +(0-4)^2 +(6-3)^2]
= sqrt(0+16+9) = 5
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.