Qe A) Find the vector 5 unit length in the direction of vector perpendicular to the iHane which passes through AC(',2,3) 1B(3,2,5) and c(!,4,-1). 2. a (1-Sino)

Q: If vector u=2i+3j+4k is orthogonal to vector v=3i+2j-bk, then value of b is 4 1 2 3

A: Two vectors x , y  are orthogonal or perpendicular if x·y=0

Q: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

Q: 1) in triple dot of vectors |(A x B). C = |(CX A). B\, where the vectors A, B, and C are not same…

A:

Q: ind a unit vector orthogonal to bothu and v. u = (-8, 7, -2) v = (-1, 1, 0)

A:

Q: What is the unit vector perpendicular aial yA n = i-j+ 3k, n2 = 2i + j + 3k to the vectors?

A: Given that:n1=i-j+3k,  n2=2i+j+3k

Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: Find the vector equation of the intersection of the plane x+2y+3z=2 and x+3z=3  r=<  ,  , 0…

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Q: u.v<0, u.w < 0 ,w .u < 0 ?

A: Given data:     The given first vector is: u. The given second vector is: v. The given third vector…

Q: Qe A) Find the Vector 5 unit length in the direction of vector perpendicu lar to the dane which…

A: Normal vector we have to find out.

Q: Express in cylindrical components: (a) the vector from C(3, 2, -7) to D(-1, -4, 2); (b) a unit…

A:

Q: The plane contains the origin and is normal to the vector&lt;4, −1, 5&gt;.

A: Given: (4, −1, 5

Q: 2 3 Let u and v %3D . Find the length of 2u and the length of -v. - Find the distance between u and…

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

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Q: Find a unit vector in the direction of vector (v= ai + bj ) and orthogonal to the vector ( u= 3i -…

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Q: Find a vector equation for the line through the point Pla,-1,0,3) that is orthogonl t the hyperplane…

A: Suppose a line passing through the fixed point with position vector a and parallel to vector b, then…

Q: Find the two vectors of length 1 normal to the plane given by the equation 3x – 2y + 4z = 7. -

A: From the plane equation we will get the direction ratio of normal. As the length of the required…

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

A: Question is solved.

Q: +C, vnere B 1s parallel to the vector (1, 2) C is perpendicular

A:

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 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: Qure O QY Use Gramer's Rule to Find Kyy and Z -y-22 = - %3D + 32 = 2 %3D 7X +y+Z = o %3D Q2/ Find…

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Q: What is the length of the vector whose initial point is (0, 1, -2) and (2, - 2, 3) 35 A. 38 В. V35…

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Q: 3 Determine the unit vectors that are nernendicular to A - and R -

A: Perpendicular vectors

Q: which vector is NOT orthogonal to (cos θ, sin θ, 1)? a) (-sin θ, cos θ, 0) b) (-cos θ, -sin θ, 1)…

A: To find which vector is not orthogonal to (cosθ,sinθ,1)

Q: s the vector ở = (-1,–2,3) perpendicular to the plane 3x + 6y – 9z + 5 = 0? %3D

A:

Q: Find the unit vector in the direction of v = (3, −1, 2), and verify that this vector has length 1.

A: Vector v = (3, −1, 2) Such that,

Q: Find a vector parametrization of the line through P = (3, -5, 7) in the direction v = (3, 0, 1)

A: Given:P=3,-5,7v=3,0,1

Q: -x + 6y + 2z = 6 1. -x + 3y + z = 7 2 Find the normal vector, n,, to -x + 6y + 2z = 6. n = 1 Find…

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Q: what is the distance between the vectors  u = (0,1,2,3) and  v = (1,0,4-1)

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Q: o v based at the origin.

A: Sketch the vector v = (2, −3) based at P = (1, 4) and the vector v0 equivalent to v based at the…

Q: Find a vector parametrization of the line through P = (0, –8, 7) in the direction v = (7, 0, 0)

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Q: 1) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

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Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

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Q: Find a vector parametrization of line through P = (9, 8, 3) in the direction v = (4, -8, 6). %3D…

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Q: Qy: In VĘ CR) find all vectors which are orthegonal to u=(1,-2, 3) uut corath

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Q: A vector is 0.888 m long and points in a 205 degree direction. Find the y-component of the vector.

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Q: Verify that the vector i = ( ) is a unit vector (that is, has length 1). Then determine the…

A: The projection of a vector w in the direction of v is given by v·wv2v

Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

A:

Q: Express the vector H %3D p?za, + зфzaф - рф*а, at B(3, -4, 1), in CCS.

A: The given vector is H→=ρ2z aρ+ 3Φz aΦ - ρΦ2 aZ.We have to express it in the cartesian co-ordinate…

Q: Find a unit vector perpendicular to plane PQR. Р(1, -1, 2), Q(2, 0, — 1), R(0, 2, 1)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Let f(x, y) = 5y² ln(4x). Then Duf(1,4) in the direction of the vector (-2, –2) is

A:

Q: Find the unit vector u in the direction of v. Verify that u| =1. 12. (1,–6)

A: solution is given below..

Q: Find a unit vector u in the direction of v = 〈6, -1〉. Verify that ⎥⎥ U⎥⎥ = 1

A:

Q: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: 9. Find both vectors of length 5 that are perpendicular to plane 2x + 2y +z - 4 = 0.

A: Explained below

Q: Find a unit vector in the xy plane that is orthogonal 2 to 4 6

A: We have to find the unit vector.

Q: 1.23. Express the unit vector directed toward the point (x, Y, z) from an arbitrary point in the…

A: Express the unit vector directed toward the point (x, y, z) from an arbitrary point in the plane y =…

Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

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Q: Express in Cartesian components: (a) the vector at A(4, 40°, -2) that extends to B(5, -110°,2); (b)…

A: express in cartesian components (a) the vector at A4,40°, -2 that extends to B5,-110° , 2 (b) a unit…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.