y–2 and = . determine the value(s) of k, such that: y-1 k–7 I+5 k The direction vectors of the lines are perpendicular [k3] The lines are parallel.[k2] 1-2 For the lines %3D %3D k+2 a) b)

Q: Q1/A/ Let u=5i-j+k, v=j-5k, w =-15i+3j-3k. Which vectors, if any, are a) Perpendicular? b) Parallel?…

A:

Q: -5 and 4 4 k are orthogonal. k =

A: We know that if two vectors u & v are orthogonal to each other then the dot product or scalar of…

Q: Find a general form of an equation of the line through the point A that satisfies the given…

A: Our Aim is to find the general form of an equation of the line passingthrough the point A(7,-3)…

Q: Consider the lines l : = 2 – y = z +1 and l2 : y - 2 3 1. Determine a direction vectors for the…

A: Consider the lines L1: x-12=2-y=z+1 and L2: 1-x2=y-2=z-33.1 To determine a direction vectors for the…

Q: nd an equation of the plane that passes through the given point and is perpendicular to the given…

A: Given point P(2,6,-9) i.e. x1=2, y1=6 and z1=-9Given vector is n=j i.e. c=1We know that equation of…

Q: O Determine if the line and plane intersect. If so, state the solution. T: -2x+6y + 4z_4=0 L: [x, y,…

A:

Q: B. A C G I. K Lines AD and HE are parallel. ZFGE = 50° ZFCE = -

A: Angle FCE is 40 degree

Q: (10) Given: x - 2y + 3z = 1 and x+y- 2z = 0 Find the line of intersection of the planes. b) Find the…

A:

Q: What are the values of h for which the vectors ar linearly dependent? HEB -4 7. h

A: Given that:  Let u=2-41, v=-67-3 and w=8h4

Q: In each part, find the two unit vectors in R² that satisfy the given conditions. 1. The two unit…

A:

Q: 2. F = (1+ 2y)i + (r + e")j, and C is the triangle with vertices (0,0), (1, 1), and (-1, 1),…

A: 2) Given vector field F→=x+2yi→+x2+eyj→. To find ∫CF.→dr→ where C is the triangle with vertices…

Q: 19. Find the angle between the line and the plane of the following equations, a. 4:r=21 +3j- k+1(2i…

A: given  :line

Q: 11. x = 11. If PQRS is a parallelogram, find the values of x and y. y : (4y + 7) 19-9 13r + 15 (10y…

A:

Q: a) Given the line X-2y = 1. Find the direction vector, V, of this line and two unit vectors parallel…

A: Question a is solved. Solving more questions which are not interlink are against the policy of…

Q: 4. Let A -(1+ m)i + 7j – 5k ,B = xî + (6 + n)f – 2k and č = (8+ m)î – 2k , %D %3| find the…

A:

Q: Q3/A/ If ā = i - 2j + k, b = i+ 2j – 4k and č = 2i – 3j + k Find: i) (ā x b). (ā x c) ii) (ā x 5) x…

A:

Q: 15. Find the Cartesian equation of the following lines: a. parallel to the line r= 2i+3j+4k +1(3i –…

A:

Q: Find Values of and e Ror the Point pC K 3, 8) that line $ = the lies the X-1 2-y = on %3D %3D Then…

A:

Q: Consider the lines e: =2- y = z +1 and l2: , = y - 2 = 3 1. Determine a direction ve ctors for the…

A:

Q: C. Find the equation of the plane passing thru P;(-1,2, –3) and perpendicular to the line through…

A:

Q: Q1. Consider the vectors A =4ax+2kay+kaz and B = 4ax+4ay-4az what value of k the two vectors. B will…

A:

Q: c) Find an equation ôf the plane that contains the point (2, 0, 3) and the line z+4 x +1 = y = .

A:

Q: Q21 ) Find the equation of the plane passes through the point P(1, 2, 3) and parallel to the…

A: Here given vectors as

Q: 3. Triangle DEF with vertices D(0, 6). E(3.5), and F(1, 1): 90° counterclockwise about the point…

A: Rotation is a rule of transformation. Through this transformation, one can produce a new image by…

Q: 2. A WTW218 student is standing on the slopes of a curiously smooth and symmetric mountain.…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Q1: The following vectors; Ā =, B = 1- Find the cross product 2- Find the angle between à and B. 3-…

A: Consider the vector, A→=1,4,-1,        B→=2,-4,6 To calculate the cross product of vector,…

Q: 3. Find the value(s) of a for which ở = (-1, 2a – 1,3) and w = (2,2a + 3,–6) are parallel.

A: Two vectors  are parallel  is their cross product  is zero. So calculate  cross product  in the…

Q: 3,

A:

Q: In space let us have the M plane: x-2y + 3z = 2 The magnitude of the angle between the l2 line and…

A: Handwriting solution provide here.

Q: L. Find the coordinates of point P with respect to the coordinate system S, where S = {0, (1/√√2,…

A:

Q: Q3: The following vectors; A =, B = 1- Find the cross product 2- Find the angle between Ā and B. 3-…

A: A→=-2, 4, 2, B→=-6, 4,- 2 1) To find: A→×B→…

Q: c) Find Proj, a. d) Find the equation of the plane (Q) passes through the point Q(-2, 1,0) and is…

A: First calculate cross product of u and v.

Q: The lines / and m have equations r 3i- 2j+ k+1(-i+2j + k) and r 4i + 4j +2k + u(ai+ bj- k)…

A:

Q: The angle between the straight line х—1 y+3 z-5 and the -1 plane 4x - 2y + 4z = 9 is a) 60 b) 90 c)…

A: From the equation of the line x-12 = y+3-1 = z-52 , we find the direction vector as  (l,m,n) = (2 ,…

Q: II. Consider the points P(1,0, 3) and Q(5, 2, -1) and the line 1: x = -7-2t y = t 2 = 9+t 1. Find…

A:

Q: Q/A/ If a = i-2j + k.b i+2j- 4k and e= 21 - 3) +k Find: i) (a x 5). (a x ) (a x5) x (a x) Q3/B/ For…

A: Here we use scalar and vector product use to solve these problems

Q: Q4. For what value of k , the vectors, v (9, k), v2 = (-3,4) are linearly dependent. Solution:

A:

Q: Ql For the vectors A=3aX-20ay + az. B=-5ax Find the O AXBXC B A.BXC © the smallest angle between…

A: Given that the vectors are       A = 3ax-2ay+az,      B = -5ax      and     C = -8az

Q: T - 1 Y - 2 2-1 Suppose the symmetric equations of lines l1 and l2 are respectively. = 2 - y = z and…

A: Here is some proble for typing these 3d problems. So i solve both the questions with clear…

Q: 3) The line L: x = 3 + 2t, y = 2t, z = t_intersects the plane x + 3y -z = −4 in a point P. Find the…

A: The equation of the line L is given as x=3+2t, y=2t and z=t. The line intersects the plane x+3y-z=-4…

Q: b. Repeat the above solution if the two vectors A and B given at a point P(r, 0, D) in space reduced…

A:

Q: Q1/A/ Let u=5i –j+k, v=j-5k, w =-15i+3j-3k. Which vectors, if any, are a) Perpendicular? b)…

A: find the dot product of u and v if the dot product is zero then vectors must be perpendicular. the…

Q: Q2: () If a= 2i-3j+k, =2 and =4 ;:find (i) (āxj) (i-j+k).(i) (2-5)-(z+5) (b) Find the distance from…

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Q: Exercise 1.4: If Ā = âx + 3ỹ and B = 5x– 2ŷ + 62 find the component of A in the direction B and 0AB

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Q: L: x = 3 + 2t, y = 2t, z =t Intersects the plane x + 3y – z = -4 in a point P. Find the coordinates…

A: The line is L:x=3+2t, y=2t, z=t Intersects the plane x+3y−z=−4 Then 3+2t+32t−t=−4…

Q: Q2. (c) Find the unit vector u that has the same direction as v= (2, 2, -1).

A: Given; vector v=(2,2,-1)

Q: 5) Make three points P, Q, and R not collinear, and (s - 2) PQ + (2s + t) QR + (s + t+ Find 3s - t.

A:

Q: (7) Find the angles between the following lines (a) r =i – 2j + (i – j) and r = 2i – 6j + µ(i – 2j);…

A:

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.