For the line that contains the points P(-1, 2, 4) and P2(3, 4, 7), find a) a direction vector. b) an equation for the line.

Q: A line L has a direction vector v =i+3j+ V6k and passes through the point Q. Find the distance…

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Q: Verify that the two lines are parallel and find the distance between the lines. L1:   x = 2 − t,   y…

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A: ANSWER IS GIVEN BELOW.

Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR is…

Q: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

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Q: Find a and b such that the lines r1 = (1, 2, 1) + t(1, −1, 1)andr2 = (3, −1, 1) + t(a, b, −2) are…

A: Given: r1=1,2,1+t1,-1,1 r2=3,-1,1+ta,b,-2 r1 and r2are parallel only if a1=b-1=-21

Q: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: Verify that the lines are parallel, and find the distance between them L1: x = 2 - t, y= 3 + 4t, z =…

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Q: Consider two lines: l1(t)=⟨6+4t, 8−2t, 2+6t⟩ & l2(t)=⟨1+4t,3−2t,4+5t⟩ a)  Do they intersect? If…

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Q: Find the direction vector of the line joining the points (a) A(7, 6) and B(-2,5), (b) with position…

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Q: Give the equation of the line in vector form, parametric form and symmetric form. The line through…

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Q: Let 0 be the angle between vectors A and B, find the value of the angle 0 when -6V3A × B = 18Ã. Ē

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Q: point for the vect

A: What point is the endpoint for the vector corresponding to T(x)?

Q: Determine whether the lines h and I, intersect, are parallel, or are skew. 1: n= 4i+3j+ (i-j+6k) 12:…

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Q: α, β and γ are the angles made by the vector with x, y and z axis respectively. The squares of the…

A: Given ,  α, β and γ are the angles made by the vector with x, y and z axisrespectively. We have to…

Q: Write a vector equation for the line segment from P to Q. 4

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Q: 4. In this figure, lines a and b are intersected by line t.

A: Answer: ∠1 ≅∠3  .

Q: If the angle between the vectors A = xâ, +â̟and B = /3â, +â, is 60°, find x.

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Q: Consider the line which passes through the point P(1, 3, -5), and which is parallel to the line æ =…

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Q: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: What is a general equation for the line with vector equation x=[31]+t[4−5]

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Q: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the…

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Q: Determine the vector equation of a line that is perpendicular to the line, p = |-4, 4, 9 + t|-1, 3,…

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Q: If a and b are two non-parallel vectors and the position vectors of P, Q and R are a + 2b, 1/2a +…

A: answer

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i, v = -3j

A: Given vectors: u=2i+0j+0k and v=0i-3j+0k u×v=ijk2000-30u×v=i0×0-0×-3-j2×0-0×0+k2×-3-0×0u×v=-6k The…

Q: If VW is not parallel to UX, what is VW?

A: Clearly from the figure we can see that the base angles are same. So this figure is an isoceles…

Q: Find a position vector that is parallel to the line x = 2 + 4t, y = 5 - 8t, z = 9t.

A: The equation of the line is: x = 2 + 4t y = 5 - 8t z = 9t From the given equation of the line we…

Q: Find the equation of one of the angle bisectors of lines l and m such that 2 %3D -2 = 8 guenfT onal…

A: If the equation of line in Cartesian form is x-x1a=y-y1b=z-z1c=λ then its vector form is…

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: For the line €: (x, y, z) = (5, - 3, 2) + n(1, 2, - 2), find a) a point of the line. b) a direction…

A: Given parametric equation of line - x, y, z = 5,-3, 2+n1, 2,-2x, y, z = 5,-3, 2+1n, 2n,-2nx, y, z =…

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i - 2j - k, v = i - k

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Q: Let / be the line through the point with coordinates (-1,2,0) in the direction of the vector Which…

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Q: For the line €: (x, y, z) = (2, 3, 4) + n(3, - 2, 5), find a) a point of the line. b) a direction…

A: the given line is: l:x,y,z=2,3,4+n3,-2,5 we have to find: (a) a point of the line. (b) a direction…

Q: Write down the line equation a) given a point Q and a vector v. b) given two points R and Q.

A: Since, our aim is to find the equation of a line that is :-(a) passing through a given point Q and a…

Q: Show that the indicated diagonal ofthe parallelogram determined by vectors u and v bisects the…

A: The given parallelogram is   Here, we are given |u|=|v| So, u+v is the required diagonal

Q: Find the vector equation of the line (d) through (6, −3) and parallel to the line through (5, −1)…

A: First, we find the slope of the line  through (5, −1) and (2, 11) Direction vector is=(2, 11)-(5,…

Q: Show that the following sets of points are collinear and find the equation of line…

A: Three or more points are collinear, if slope of any two pairs of points is same. With three points…

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i - 2j + 4k, v = -i + j - 2k

A: Given: The vectors, u=2i-2j+4k and v=-i+j-2k.

Q: Find an equation for the line through P(11,10) parallel to vector v=2i-3j

A: Given point on the line is P(11,10) The vector parallel to the line is,v=2i-3j

Q: find the length and direction (when defined) ofu * v and v * u. u = i + j - k, v = 0

A: Consider the given vectors and rewrite vector v in terms of i, j and k. u=i+j-kv=0v=0i+0j+0kTo find…

Q: Here is a drawing of vectors a, b, and c. 18 ć Which equation correctly describes a in terms of b…

A: Given drawing of three vectors.

Q: A line L has a direction vector v = i+ 3j+ V6k and passes through the point Q. Find the distance…

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Q: Find the z-coordinate of the foot of the perpendicular from A(1, 1, 1) on the line joining B(1, 4,…

A: We will solve the problem.

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: Prove that the lines r = (1, 2, −1) + t(2, 2, 1) and r = (−1, −2, 3) + s(4, 6, −3) intersect, and…

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Q: For Exercises 17 and 18, find the acute angle between the given lines by using vectors parallel to…

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

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…