Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are parallel and find the distand %3D between them. NOTE: Enter the exact answer. L1 and L2 are parallel because they are parallel to vectors vị and v2 that satisfy : Choose one ▼

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

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Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find b.…

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Q: If r1,r2 and r3, are three parallel vectors of the same magnitude, Prove that r1+r2+r3 is equally…

A: GIVEN: r1 , r2 , r3 are three parallel vectors

Q: 4x-y+5z=0

A: If a line and a plane are perpendicular to each other then the direction vector of the line and the…

Q: In triangle ABC a line is drawn from A to the midpoint of BC, labelled D. Prove that vectors…

A: The solution is given by using triangle law of vectors as follows

Q: Given that vectors p and q are perpendicular, where p≠0 and q≠0 show that |2p+3q|²= 4|p|²+9|q|²

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Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+k %3D %3D %3D where a = 2, b…

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Q: Consider two vectors A and B prove that the cross product between them can be calculated as follows…

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Q: Verify that the two planes are parallel. -x + 6y + 2z = 8 -x + 3y + z = 9 2. Find the normal vector,…

A: Find your answer below

Q: If r1,r2 and r3, are three parallel vectors of the same magnitude, Prove that ri+r2+r3 is equally…

A: given

Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

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Q: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

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Q: If a = 2i -j+2k and b =i+2j-2k, find two vectors c and d satisfying all the following conditions:…

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Q: 14. The accompanying figure shows nonzero vectors v, w, and z, with z orthogonal to the line L, and…

A: Given V and W make any equal angle with L. |v| = |w| Z and L are orthogonal to each other.

Q: A line L has a direction vector v = 2i + 4j + V5k and passes through the point Q %3D Find the…

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Q: Consider the points P(3, x, -2) and Q(5, 3, 4) in R3 . Find x so that the vector from P to Q is…

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Q: 16. The accompanying figure shows nonzero vectors v, w, and z, with z orthogonal to the line L, and…

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Q: Given v = 2i + j, w = 6i + 3j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

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Q: ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express…

A: Given P,Q are the mid-points of 2 sides AB,AC of the triangle ABC. Also, AB=2x, AC=2y.

Q: The vectors A 6i + 4j – 8k and B = xi + 6j + zk are known to be parallel. Find x and z x = 9. -12

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Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

A: Given  AB=i+4j-2k and B is the point (5,1,3)

Q: Let L be the line 8x + 2 in R?. Find vectors a and b so that v a + tb with t ER is also a correct…

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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: * For the vectors v=16,8) and W=18,6), validate the Schwarz and Triangle mequaiity and fino the…

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Q: The plane that contains the point (3, –1, -4) and the line with equation y – 1= 3z is orthogonal to…

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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: Prove that the intersection line of the planes P₁: 2x -y - 2z = 0 and P₂:x-2y+z = 0 is parallel to…

A: Since you have posted multiple questions and we can answer one question. So, answered the first…

Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: If a, b, and c are constant vectors, r is the position vector zi+ yj+ zk, and Eis given by the…

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Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: 2. Given two non-parallel lines l1: r = 2+t, y = 4+t, z = 8, and l2: x = 3, y = 2 + t, z = 5+t, (a)…

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Q: If two vectors p and q are such that |p| = |q, show that p + q and p- q are (This proves that the…

A: Given p=qwe know that two vectors are perpendicular iff their dot product is zero

Q: Define the line Lo to be a = xo + at, y = yo + bt, z = z0 + ct. If Lo passes through the origin,…

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Q: Given v = 3i - 2j, w = 2i + j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A: Given that, The vectors  v = 3i - 2j, w = 2i + j. We have to find projw v By using a formula, projw…

Q: Consider a point Q(x1, y1, z1) and a line L given by the vector equation r = r0 +tv,where r0 =…

A: First obtain a, where a is the distance between R0 and Q.

Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

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Q: A line L has a direction vector v = 2i t 4j+ v5k and passes through the Find the distance between…

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Q: For the vector PP, , its norm satisfies PP, =2. The inscribed angles between PP, 2 2 and x-axis and…

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Q: Let the vector ū = (k,5,–1) and v = (2k,k,3) are perpendicular in R', find the value of at related…

A: Given: u→=k,5,-1v→=2k,k,3

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: Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose…

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Q: For the non-zero vectors A and B to be perpendicular to each other, the necessary and sufficient…

A: Given, For the non-zero vectors A and B to be perpendicular to each other, the necessary and…

Q: Find the vectors that satisfy the stated conditions. 23. (a) Oppositely directed to v (3,-4) and…

A: a) The given vector is v = <3, - 4>  To find vector opposite to given vector and half in…

Q: Consider the lines 3 - z x – 5 l1 : 2 and I. Find two unit vectors that are parallel to l1.

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Q: Draw a diagram to illustrate point R divides line PQ such that PR=RQ and R is the midpoint of PQ,…

A: Concept: Vector: A vector is a -dimensional entity with significance and course. A vector may be…

Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.

Q: Prove that in R², the vectors {v1, v2, V3} are always dependent. What about if we have two vectors…

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