1. Given the following lines: 3x D:: * = y – 1 Dz: x+ y-6 = 0 a-) Give a normal vector associated with each of these lines. b-) Find the measure in degrees of the acute angle between these lines.

Q: Find the ualt noima vector fol for Rhe Lvector valuhed P(4)=t t? and sketch the durve the vector…

A: To Find:

Q: 1or Find. Ewo unit Vectors in X-y plane 30 deyree with the vectur that make angle cf V= 3i +4j ?

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Q: Is the line x = 6- 3t, y = 8 + 8t, z= -t parallel to the plane 3x + y -z=2? Give reasons for your…

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Q: H=pz Csup ap te'sin dg tpan 2 At point (1, ,6)

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Q: For y'= Aj where A is given below %3D A= find the right hand side vector F(t, ) needed to apply…

A: Given y'→=Ay→ Here A=1245 We have to find right hand side vector F→(t,y)→.

Q: Let vector v = 3i – 2j+ 4k and point P = (0,0, -3). For what point Q is it true that v = PQ?

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Q: If is a smooth curve given by a vector function r(t) a < t < b and is a constant vector, show…

A: So we have;

Q: Show that at every point on the curve r (t) = ⟨et cos t, et sin t, et⟩ the angle between the unit…

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Q: For a plane with a normal of n = [1, 2, - 9]   and containing a point P (3, -4, 0), write the…

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Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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Q: Show that the lines L1 : x =1– t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y= 3 – 6t, z = 5 – 3t are…

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Q: If v = (1,2 ) draw all vectors w = (x, y) in the xy plane with v · w = x+ 2 y = 5. Why do those w's…

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Q: if A=i+j+X, B=zi-j+3ksfind vector normal to B and in plane of A and B- ans. $2(3i+9j+x)

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Q: Show that at every point on the curver(t) = ⟨et cos t, et sin t, et ⟩ the angle between the unit…

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Q: Fix a point P on the line ( and let N be normal unit vector to (. Show 5. (. that if N' is another…

A: Given: A fixed point P on the line l. An unit vector N normal to l.   To show: If N' is another unit…

Q: at Q6:- If w = xi + yj + zk nonzero vector. Then show that cos a + cos? B + cos? y = 1, where a, B…

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Q: If possible, determine the vector, parametric,symmetrical and reduced line r that: a) passes…

A: Given the lines S1:t·1,2,3, t∈ℝ and S2:y=x+2, z=x. To find a line L passing through the point P1,1,1…

Q: Suppose that C has length 5. What is the value of F. dr if: (a) F(P) is normal to C at all points P…

A: Given: Length of C is 5. (a) F(P) is normal to C at all points P on C. ∫CF→·dr→=∫CFdrcos90°=0…

Q: 1. Given the time_Varying position Vector x iat+jbt2+Kct z where ast,b=2,andc=3_are Gnstants. hind…

A: Given : a=1, b=2, c=3 x = iat+jbt2+kct3

Q: A particle's position vector is given by: F(t) = R(1+ cos(wot + q cos wot))& + R sin(wnt + q cos…

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Q: 19. Suppose that the normal unit vector N of a surface S at z =f (x,y) is determined, how does the…

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Q: 3. Prove by the analysis of orthogonal trajectory that the lines Ax + By = C and Bx – Ay = k are…

A: let slope of line Ax+By=C is m1By=-Ax+Cy=-ABx+Cso m1=-ABslope of line Bx-Ay=k is m2Ay=Bx-kso…

Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope…

A: We first have to find the slope of the given vector and the line. If the slopes are equal then they…

Q: Given the unit tangent 1 (-2 sin t, 1, 2 cos t), V5 U = and unit normal vector: n = (– cos t,0, –…

A: We are given  unit tangent vector ,u=15(-2 sin t,1,2 cost) and unit normal vector, n=-cost,0,-sin t…

Q: W,X ,Y,and  Z have the position vectors 3i+3j-4k, 4i+j+k, 2i+3k and 3i+j-4k respectively.…

A: The given position vectors areW = 3 i^ + 3 j^ - 4 k^X = 4 i^ + j^ + k^Y = 2 i^ + 3 k^ Z = 3 i^ +  j^…

Q: Find equations of the following. 2(x – 7)2 + (y – 5)² + (z – 6)² = 10, (8, 7, 8) %3D - (a) the…

A: Suppose we have given a surface .Then; The equation of tangent plane at   is  . The equation…

Q: ARST is reflected across a line so that T'has coordinates (1, 3). What are the Coordinates of S'? R…

A: Given: R=-4,4S=0,-2T=-3,-1

Q: By vector methods show that the line x = y = (1/3)(z + 2) is parallel to the plane 2x - 8y +2z = 5..

A: Any arbitrary point P0 on the line can be determined to be as:

Q: Find the equations of the tanget plane and normal line to the graph of In(z?) x - = 3y3 – Vx at the…

A: tangent plane and normal line

Q: The unit normal vector to the surface x'y + 2xz? = 8 at the point %3D (1,0, 2) is

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Q: Suppose that n is normal to a plane and that v is parallel to the plane. Describe how you would find…

A: Consider the given information as n is normal to a plane and that v is parallel to theplane.

Q: find the distance d(u, v) between u and v in the given exercise.

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Q: Given: planes Π1 : 2x − 5y + z = −1 and Π2 : x + 5y + z = 5 intersecting on a line ℓ. (a) Compute…

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Q: Given f(x.y.:)=9x² – 5:-7+xy and Vf = (18x+ y,x,-5). Find a unit %3D normal vector at point P =…

A: As ∇f is the gradient of the surface f , it will point towards the normal vector of the surface.

Q: ir kümelerinden kaç tanesi R' için bir tabandır? how many of the given vector

A: A subest S of R2 is a subspace if and only if it contains the null vector whenever it contains two…

Q: Find the point on the graph of z = 3x2 + u? at which vector n (24, 2, –1) is normal to the tangent…

A: Gradient of the surface denote the normal direction.

Q: Given the unit tangent 1. (-2 sin t, 1,2 cos t). V5 and unit normal vector: n=D(-cost,0, - sin t).…

A: Given unit tangent  u=15-2sint, 1, 2cost and unit normal vector n=(-cost, 0, -sint) To find the unit…

Q: Show that A(x - x0) + B( y - y0) = 0 is an equation for the line in the xy-plane through the point…

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Q: By vector methods find the angle between the line x = y = 2z and the plane x + y + z = 0.

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Q: Find the principal unit normal vector for the helix r(t) = 2 cos ti + 2 sin tj + tk.

A: Given, r(t)=2 cost i+2 sint j+t k

Q: In R', Find the unit vectors that are parallel to the tangent line to the curve y = 2 sin x at the…

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Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: B- Find the length of the curve given by the position vector r=, =r'i+(1+(1/3)x')j+(1-(1/3)')k for

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Q: Find the point on the graph of z = 3x2 – 3y? at which vector n = (48, –60, –2) is normal to the…

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Q: Given the following points, determine the vector equation defined by having point A as initial point…

A: RCS- Rectilinear Co-ordinate System CCS-Cylindrical Co-ordinate System SCS- Spherical Co-ordinate…

Q: Suppose a line is given parametrically by the equation L(t)=(1-t, t-4, 1-t) then the vector u and…

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Q: Let h VI and y: 8 For what value(s) of h, is y in the plane generated by vị and v2?

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Q: Let Q be a point in R°. Consider a line passing through P with direction vector d. What is the…

A: Please check image in step 2