Answer all as they are small question answer True/FalseIndicate whether the statement is true or false.9. A normal vector to a line is parallel to that line.10. There is no symmetric form for the equation of a plane.11. A plane written in scalar form can be written in vector form.12. In three-space there are two possibilities for the intersection of two lines.13. A line will never intersect with a plane.

We have to state whether the given statements are true or false: Statements are as follows: 9. A…

Answered: True/False Indicate whether the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 31E

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Similar questions

Does the sphere x2+y2+z2=100 have symmetry with respect to the a x-axis? b xy-plane?
1.) is the quantity r(t+h)-r(t) a vector or a scalar? identify this object in the applet. 2.) is (r(t+h)-r(t))/h a vector or a scalar? Describe what represents r(t+h)-r(t)/h 3.) slide h toward to 0. How does r(t+h)-r(t) change? How about (r(t+h)-r(t))/h?
If false explain why. Justify your answer. True or False: “Let L be a line in R3 with direction vector d, and let P be a plane with normal vector n. If n · d = 0, then P and L intersect.”
Please look at the attached image as its clearer Suppose the straight lines L1�1 and L2�2 have respective vector equations r1=⎛⎝⎜4−33⎞⎠⎟+t⎛⎝⎜5−11⎞⎠⎟andr2=⎛⎝⎜98−2⎞⎠⎟+s⎛⎝⎜−5−52⎞⎠⎟,�1=(4−33)+�(5−11)and�2=(98−2)+�(−5−52), where s� and t� are scalar parameters. a) Given that L1�1 and L2�2 intersect at some point P�, find its coordinates. P=�=(,,) b) Find the exact value of the cosine of the acute angle θ�, between L1�1 and L2�2. cosθ=cos⁡�=
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How would I solve this problem? Find the coordinates of a point P on the line and a vector v parallel to the line. (x-9)/4 = (y+3)/3 = z + 8 (image attached)
Represent the plane curve by a vector-valued function. (There are many correct answers.) 3x + 8y − 24 = 0
D) What is the correct description of the coordinates of all vectors in the three-dimensional space? Who are in the yz plane (or parallel to the yz plane)? I) x is a constant, y E R, ZE R Ii) XER, Y = Z He) X E R, y and z are constants Iv) x=0, yER, ZE R
1. What is the normal vector of the plane x + y - z = 1? 2. Foe what values of a and b are the vectors u = (2a, -b, -1) and v = (4, 3a - b) equal? a. a = -5; b = 14 b. a = 5; b = -14 c. a = -5; b = -14 d. a = 5; b = 14 3. Which of the following is not true? a. (u • v) + w = u • (v + w) b. u • (v - w) = u • v - u • w c. (u - v) • w = u • w - v • w d. (u + v) • w = u • w + v • w
An elliptic cone in R^3 is described by the equation c^2 = (a + 2)^2 + b^2/9 . a. Find an equation for the tangent plane to the cone at the point (1, 12, −5). b. Does the tangent plane exist for every point on the cone? c. The tangent space at a point on a graph in R^2 is a line. The tangent space at a point on a surface in R^3 is a plane. As was the case for surfaces in R^3, the normal vector can be used to describe the tangent space to graphs in R^4 . But, the tangent space is no longer a plane. What does this tangent space look like?
1.Find the distance between the parallel planes 2x - y - z = 5 and -4x + 2y + 2z = 122.What is the normal vector of the plane x + y - z = 1
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