Suggest a "vector proof" of the fact that, inR2, two lines with slopes m1and m2 are perpendicular if and only if m1m2 =- 1

Q: Choose a set S of three points such that aff S is the plane in R3 whose equation is x3 = 5. Justify…

A:

Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: show.. that the line in.which. the planes.X+zy-223D5 and. 5X-zy.-7=D0.jntersect.is. pavalle.to. the…

A:

Q: Suppose that L1 is the line through point (1, 2, 3) with direction vector [2 ,- 3 ,0]t. And suppose…

A:

Q: Show that the lines determined byr 1(t) = <−2 − 5t, 3 + 2t, 4t >andr 2(t) = <8 + 15t, 1 −…

A:

Q: Use vectors to show that the distance from P1(x1, y1) to the line ax + by = c is d = |ax1 + by1 -…

A:

Q: Show that the lines L1 : x = 5 – t, y = 2t, z = 5+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

A:

Q: Show that the vector v = ai + bj is perpendicular to the line ax + by = c by establishing that the…

A:

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(3, 4, 5) P2(2, 3,…

A:

Q: Show that a set of vectors {v,, v2. ..., V5} in Rn is linearly dependent when dim Span {v,, v2, ...,…

A: We need to show that: {v1, v2, v3, v4, v5}  in Rn are linearly dependent when  dim Span{v1, v2, v3,…

Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

A:

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…

A:

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…

A:

Q: what is the vector equation of the line of intersection of the planes z=5 and x=9

A:

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

A:

Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: Find a vector parallel to the line of intersection of the planes 2x + y - 3z =13 and x + 3y + 5z =-8

A: Given, The equation of the planes  2x+y-3z=13 x+3y+5z=-8 We have to find a vector parallel to the…

Q: Find an equation of the plane that passes through the point P(-4, -5, 4) and has the vector n =…

A: Plane passes through the point P-4, -5, 4 and has the vector n=-4, 9, 4 as a normal.

Q: Suppose L1 and L2 are disjoint (nonintersecting) nonparallel lines. Is it possible for a nonzero…

A: Given:

Q: Find the vector, parametric, and symmetric equa lines: (a) the line perpendicular to x+7_y-4 with 3…

A:

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: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

A:

Q: Construct a geometric figure that illustrates why a line in R2not through the origin is not closed…

A:

Q: Show that the lines x = p + su and x = q + tv are skew lines. Find vector equations of a pair of…

A: Consider the matrix values given. The equation can be written as :

Q: Show that the lines L1 : x = 4 – t, y = 2t, z = :5+t and L2 : x = 1 + 4t, y = 3 – 8t, z = 5 – 4t are…

A:

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…

A:

Q: Use vectors to prove that the line segment joining the midpoints of two sides of a triangle is…

A: Using Vectors, Our Aim is to prove that the line segment joining the midpoints of two sides of a…

Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: Give an example of a linear combination that resulted in the zero vector that did NOT have 0's for…

A: Query- Give an example of a linear combination that resulted in the zero vector that did NOT have…

Q: Find the equations of the tanget plane and normal line to the graph of In(2?)x-을=3y3-VE at the point…

A: Equation of tangent plane f(x, y, z) = k at x0, y0, z0 is, fxx0, y0, z0x-x0+fyx0, y0, z0y-y0+fzx0,…

Q: Find a vector perpendicular to the 2-space line: Qx - Ny + R = 0

A: Please see the below picture for detailed solution.

Q: Show that direction vectors of the lines x-3y+ 1 L: and 2 -2 are orthogonal.

A: Direction vector of a line x-x1a=y-y1b=z-z1c   is   <a,b,c>  So, Write the direction vector of…

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

A:

Q: Show that ū = aitbj is perpendicular to the line ax+by=C by establishing that the slope of the…

A:

Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: Suppose that Tui, Tus As lineady independent (Here, TELLU, W)) Prove that vi, Vz is linearly…

A:

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. P1(1, 4, 5) P2(4, -2,…

A: Given that P1 1, 4, 5   and  P2 4, -2, 7. Compute the direction of vector P1P2 as follows.…

Q: State the difference between a position veetor and a line vector.

A:

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

A:

Q: Show that direction vectors of the lines 2 - 2 and L: are orthogonal.

A: The given lines are x-32=y+14=z-2-1  and x-35=y+1-2=z-32. The direction vectors of the given lines…

Q: Use a directed line segment to represent the vector.u = (2, −4)

A:

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

A: Let's find.

Q: Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to…

A:

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

A:

Q: Show that direction vectors of the lines L: and are arthogonal.

A:

Q: Use a directed line segment to represent the vector.u = (−3, −4)

A: The directed  line segment is the vector drawn from the any two points in the cartesian plane. The…

Q: Show that the lines with vector equations L1: 7 = (-2,1,0) + s(1, –1, 1), s ER L2 : 7 = (0,1,0) +…

A:

Q: Suppose that II1 and II2 are parallel planes in R³, given by: II : ajx + biy +cjz = d1, and II2 :…

A: If ∏1: a1x+b1y+c1z=d1 and ∏2: a2x+b2y+c2z=d2 are parallel planes, then, the cross product ∏1×∏2=0.…