Let L1 be the line passing through the points Q1(1, 1, 1) and Q2(4, −5, −8) and let L2 be the line passing through the point P1(−10, 9, 14) with direction vector d=[−3, −1, −1]T. Determine whether L1 and L2 intersect. If so, find the point of intersection Q.

Q: Find a plane containing the point (6,-7,7) and the line x(t) y(t) z(t) = = = - 2 - 6t - 1 + 5t 5-t

A: Here we have to find the equation of plane

Q: For which value of z the set of vectors is a linearly dependent set in R2? 3. Select one: -2 3. none…

A: Option A is correct option. x= -2

Q: Let L, be the line passing through the point P=(8, -6, 0) with direction vector a=-3, 3, 1]", and…

A: Given, L1 is the line passing through the point P1=8,-6,0 with the direction vector d1→=-3,3,1T. So,…

Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

Q: Determine the value of k for which the direction vectors of the lines x+3 Z = y = -1 are…

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Q: Let L7 be the line passing through the points Q1=(5, -5, -1) and Q2=(3, -3, 5). Find a value of k so…

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Q: Show whether R³ of the set B is a base and find the coordinate vector of the vector u = (- 1, -5,9).

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Q: Determine whether u = is a linear combination of vị and V2

A: Here given that                        u=213 , v1=13  and v2=2-1 Now we determine that u=213 is a…

Q: Let L1 be the line passing through the point P1=(3, 13, 13) with direction vector →d1=[1, 3, 2]T,…

A: Shortest distance

Q: Let L7 be the line passing through the point P1=(1, 3, 7) with direction vector d= [-2, -2, 2]", and…

A:

Q: Find the point on the graph of z: (x2 + + 4y") at which vector n = - P =

A: Given,  (a)   z=-x2+4y2,   n=8,-80, 2  (b) f(x, y)=ex2+2y at (0, 0)

Q: Q6: For every two lines intersecting in space, there is only one plane in them True false

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Q: Use the function to find the image of v and the preimage of w. T(V,, V21 V3) = (4V2 - V1, 4V1 +…

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Q: Let L1 be the line passing through the points Q1=(-1, 1, 3) and Q2=(0, 2, 5). Find a value of k so…

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Q: show that the given vector functions are linearly dependent on (−∞,∞).

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Q: Let Lj be the line in R³ which is given by the vector equation p = s + Let L2 be the line in R³…

A: Given that  L1 be the line in R3 which is given by the vector equation  p=s110+100 L2 be the line in…

Q: Let L₁ be the line passing through the point P₁=(5, 2, 3) with direction vector d=[1, 3, 1]', and…

A:

Q: Let L7 be the line passing through the points Q1=(3,-5, –1) and Q2=(0, 4, –10). Find a value of k so…

A: Given that L1 be the passing through the points Q1=(3,-5,-1) and Q2=(0,4,-10). And the line  L2 be…

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4v1 +…

A:

Q: If possible, determine the vector, parametric,symmetrical and reduced line r that: a) passes…

A: Given the lines S1:t·1,2,3, t∈ℝ and S2:y=x+2, z=x. To find a line L passing through the point P1,1,1…

Q: Determine whether the following vectors are linearly dependent or independent and find a linear…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: (b) 4x Find any values of x such that the vectors 3 and are parallel X-1 to each other.

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Q: Show that the condition that the curves ax²+by²=1 a'x?+b'y²=1 1 1 1 1 Should intersect orthogonally…

A: If m1 = tangent at point (x,y) and     m2 = tangent at point (x,y) then Orthogonal conditions is…

Q: Let L, be the line passing through the point P(-3,-5,-6) with direction vector d-[1,0,-1]", and let…

A: Line L1 passes through the point P1=(-3, -5, -6) with direction vector d1→=1, 0, -1T. ⇒L1: r→=(-3,…

Q: Let L1 be the line passing through the points Q1=(4, 1, 5) and Q2=(0, 3, 7). Find a value of k so…

A:

Q: Let L7 be the line passing through the point P-(-19, –9, –10) with direction vector d=[3, 2, 1]',…

A: Here we find the point q1 and q2 and shortest distance.

Q: Use the function to find the image of v and the preimage of w. V2, V1 + V2, 2v, – v2 2 v = (5, 5), w…

A: Here we have a function,we have to find image of v and pre image of w.

Q: Consider the vectors V1, V2, V3 and b. 1 2 8 -2 V1 ,V3 -13 6. 12 18 Write b as a linear combination…

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Q: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

A: Let S = {v1, v2, v3} be a set of linearly independent vectors in R^3. (a) Are the vectors in the set…

Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Let F = x i+ (x + y) j+ (x - y + z) k. Let the line I be a = 3t – 4, y = 3t – 3, z = 2t – 2.

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Q: OABD is a square and the line segment OA, OB, OC a re represented by the vectors a, b, c…

A: In this question we will use laws of vector addition

Q: determine whether the members of the given set of vectors are linearly independent for −∞ < t…

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Q: For which real values of A do the following vectors form a linearly dependent set in R³? vị %3D 1 V2…

A: since given vectors are linearly dependent.

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

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

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Q: Show that the set is linearly dependent by finding a nontrivial linear combination of vectors in the…

A:

Q: Let S = { t² + 1, t² – 1, t – 2}. - 2. If S is linearly independent in P2, write 2t2 – t + 5 as a…

A: Three vectors A,B,C are said to be linear dependent, then there exist three numbers a,b,c such that…

Q: let L1 be the line passing through the points Q1=(2,1,1) and Q2 = (-4,10,7). Find the value of k so…

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Q: Let Lz be the line passing through the point P;(2, -5, 4) with direction vector d=[1, 1, 3]", and…

A: Here we calculate the distance between two line using differentiation.

Q: Find the maximum and minimum values, and a vector where each occurs, of the quadratic form subject…

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Q: Define T:R –→ R² by T ¤1 – 6x2 12 2x1 – 12x2 . The range of T is The span of a single vector: O {0}…

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Q: Given the functions 2x and |x|, show that (a) these two vectors are linearly independent in C[−1,…

A: (a)  The linear combination of two given functions is  2xc1 + xc2 Now , put x=1 and -1, we get two…

Q: Q2) The seraight s line (1,0, 1) +e(2,1,1) intersect The plane X+2y-3#=0 at the point (O,O. D)

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Q: Which of the following sets is always linearly dependent? :{V1, V2} where the equation a1V1 + a2V2 =…

A: According to the given information, it is required to tell which of the following sets are linearly…

Q: Let L7 be the line passing through the points Q1=(2,-2, 2) and Q2=(0, 1, 4) and let L2 be the line…

A: