Compute the orthogonal projection of i = 1 onto the line L through 4 and the origin. projz (5) =

Q: Consider the vectors i = (2, – V3, 1) and ū = (-1, v3, 4). Find the orthogonal decomposition of u…

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Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: The image of (-2 , 5) under reflection y = -x followed by translation with translation vector (-3 ,…

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Q: Compute the orthogonal projection of 7 = proj,(v) = 4 [1] onto the line L through -4 and the origin.

A: Given:    Data is given

Q: Compute the orthogonal projection of v= 7 onto the line through 4 2 and the origin.

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Q: Compute the orthogonal projection of u onto 7. Use the square root symbol 'V' where needed to give…

A: Orthogonal projection

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: We have, Equation of plane through P0 =(x0, y0, z0) with normal vector n = <a, b, c> Vector…

Q: Find terminal point Q of vector PQ =    <9, −2, 1>   with the initial point at…

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Q: Find the scalar equation for the plane passing through the point P=(-5, -2, –4) and containing the…

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Q: Compute the orthogonal  projection of v = [ -3, -3 ] onto the line L through [ 2, -2 ] and the…

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Q: Find a vector equation for the line segment that joins P(1,3,4) to Q(-2,4,6)

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Q: Find the scalar equation for the plane passing through the point P-(5, 3,-5) and containing the line…

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Q: The orthogonal projection of v = 10i on b = −3i + j is _____ .

A: To find the orthogonal projection of v = 10i on b = −3i + j .

Q: find a vector parametrization for the line with thegiven description. Passes through O and (4, 1, 1)

A: To findvector parametrization passes through O and (4,1,1)

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

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Q: 6. Find the distance of the point (-1,1) to the line given in vector form (x, y) = (2,0) +t(4, 3).

A: Given that: The point is (-1, 1).The vector is:  (x, y)=(2, 0)+t(4, 3)

Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

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Q: Find the vector equation of the line that passes through point M(1, 1, 2), intersects the following…

A: Question is solved.

Q: 3) Write down the equation of line in a vector parametric form, scalar parametric form and standard…

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Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

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Q: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: Find the cross product ⃗a × b and then specifically verify that it is orthogonal to both ⃗a and b:…

A: Given data:     The first vector is: a=<a1, a2, a3>=<6, 0,-2> The second vector is:…

Q: Find a vector equation for the line segment connecting the points P = (-9,–6, 8) and Q = (-15,…

A: We have to find a vector equation for the line segment connecting the points P=-9,-6,8 and…

Q: Find a vector orthogonal to the line x+y=1

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Q: 3. Write the scalar equation for a plane passing through (5,8,-1) and perpendicular to the line x =…

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Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

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Q: Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3,…

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Q: Compute the orthogonal projection of v = [-6   5   1 ]   Onto the line L through [ -2   6   -7] and…

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Q: 3. When origin is shifted to (3,4) by translation of axes, find the transformed equation of 2x² +…

A: We have to solve given problems:

Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

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Q: 21. Apply the conjugate-gradient method to the problem Ax = b, where 1 A = 1 1 %3D and b = 1 Verify…

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Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)

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Q: Compute the orthogonal projection of v = 3 onto the line L through -2 and the origin. projr (7) =

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Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

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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: Compute the orthogonal projection of i = onto the line L through and the origin. proj, (1) =

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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: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

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Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

A: The equation of plane with normal vector (a,b,c) passing through the point p0 =(x0 ,y0 ,z0 ) is…

Q: ) Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

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Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: The vector E = = -a, – 4as + 3a, expressed in RCS and in terms of ø is Е 3 (-сosф + 4sinф)ax +…

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Q: The orthogonal projection of v = 10i on b = –3i + j is <

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Q: Give the vector equation of the line passing through P and Q.P = (1, 1, 0), Q = (1, 0, 1), R =…

A: P=(1,1,0) and Q=(1,0,1)we have to find vector equation of the line passing through these points

Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

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Q: 1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x =…

A: The given equations of lines are: L1:x=5-2t, y=-7+t, z=6+4t and L2:x=2+3t, y=5+2t, z=1+t Rewriting…

Q: Find the orthogonal projection of the vector b =-1 on Nul(A), where -2 -2 3 -10 A = 1 -1 2 3 1 -3 3…

A: For the solution follow the next steps.

Q: Find an equation of the plane that passes through the point P(4, 5, 3) and has the vector n = (1, 8,…

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