Determine the vector, parametric, and Cartesian (Scalar) equations for the line that passes through A(4, – 1) and is perpendicular to the line through points M(-4,3) and N(2,0).

Q: Find the vector parametric equations for the line. in the direction of the vector – i+ 5j-3 k and…

A: equation of line in vector parametric form

Q: Find the vector form of the equation of the line inR3 that passes through P = ( -1, 0, 3) and is…

A: Equation of a line passes through  x1, y1, z1 having direction ratios a, b, c is, x-x1a=y-y1b=z-z1c

Q: Find the component form of the vector v, (a) write the vector using standard unit vector notation,…

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Q: Find the vector equation of the line of intersection, if it exists, for each pair of planes. a. 2x…

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Q: Find the distance of point A(2/3, 2) from the line that passes through the origin and parallel to…

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Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x= 2+3t y…

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Q: 4 - x y + 1 %3D 2 1 3 L2 :[x, y, z] = [-2,4,3]+ t[-6, 5, 7], t E F

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Q: Find a vector equation with parameter t for the line through the point (7,0, –7) and parallel to the…

A: We have to find a vector equation with parameter t.

Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2+3t y…

A: Given, The parametric equation of the line D passing through A and parallel to vector v is  x =…

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

A: point = (3,5,-7)n=0 i +1 j + 0 kCartesian equation of plane is Ax+By+Cz+D=0(A,B,C)=( 0,1,0)(x,y,z) =…

Q: O Find the parametric equation of the line through the point (-3,1,6) parallel to the vector V 2i +…

A:

Q: Find the parametric equation of the line that passes through the point P(2,4, –2) and is parallel to…

A: Parametric equation of line that passes through the point P(x0, y0, z0)& parallel to vector a =…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar -7w.

A: Given: u=2i-5jv=-3i+7jw=-i-6j

Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: 4u.(5v - 3w)

A: Given: u = -i + j, v = 3i - 2j, and w = -5j

Q: M contains the point with coordinates (0,0,1) 2 M is orthogonal to the vector 0

A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar 3w + 2v.

A: Given: u = 2i - 5j, v = -3i + 7j, and w = -i - 6j

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

A:

Q: Let u = -2i + 3j, v = 6i - j, w = -3i. Find the specified vector or scalar 4u - (2v - w)

A: Given: u=-2i+3j , v=6i-j , w=-3i

Q: 22. Given the symmetric equations t = - and t = +', find the vector equation of the line.

A:

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: Given, Normal,n=(2,-4,1) Point, P=13,23,1     Find the equation of the plane with normal vector n…

Q: Find a vector equation and a parametric equation for the line that passes through the point (5, 1,…

A: We have to solve given problem:

Q: Find the vector parametric equations for the line. in the direction of the vector 57-5-k and through…

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Q: Let v = -5i + 2j and w = 2i - 4j.Find the specified vector scalar, or angle 3v - 4w.

A: It is given that, v = -5i + 2j and w = 2i - 4j

Q: Find a scalar equation for the plane that contains the points P, Q and R

A: We know that equation of plane passing through three points A(x1,y1,z1),B(x2,y2,z2), C(x3,y3,z3)  is…

Q: Let u = -2i + 3j, v = 6i - j, w = -3i. Find the specified vector or scalar 3u - (4v - w).

A: Given- u=-2i+3j,v=6i-j and w=-3i To find- 3u-4v-w

Q: Consider the vector y = [1 2 3]. Find the orthogonal projection of y onto the plane x, - 2x2 + 4x3 =…

A: Given vector is y=1,2,3 Given plane is x1-2x2+4x3=0 Normal vector to the p[lane is n=1,-2,4…

Q: Find parametric equations for the lines in The line through (2, 3, 0) perpendicular to the vectors u…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: a) Find the scalar parametric form of the equation of the line which is parallel to the line of…

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Q: Find a vector perpendicular to the graph of z = - 3 x2 + 9 y2 – 7 x y at the point (8, 2, -268).

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Q: Find a vector parametric equation (t) for the line through the points P = (1, −4) and Q = (−2, −9).

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Q: find the two-dimensional vector equation of the line r(t) = a +t*m such that - r(0) has norm 8 and…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(0, −1,…

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Q: Find the scalar equation for the plane passing through the points P1(2, 1, 5), P2(2, 0, 9), and…

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Q: A parametric equation of the line (D) passing through A and parallel to the vector v is: x = 2+3t…

A:

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar -4w.

A: Given that : The vectors  u = 2i - 5j, v = -3i + 7j and w = -i - 6j .

Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: 5u.(3v - 4w)

A: Given: u=-i+j, v=3i-2j and w=-5j

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( – 1,…

A: find the explanation below

Q: Find a vector equation of the line r through D4 and perpendicular to the line s through F4 and B1.…

A: Given,D4→ = 1i ^ + 2j^ + 3k^Equation of line passing through D4→ is:x-1a= y-2b=z-3cThe above line is…

Q: Find a vector equation and parametric equations for the line segment that joins P to Q, given P(0,…

A:

Q: Find the vector equation that represents the curve of intersection of the paraboloid z = 4x2 + y and…

A: The given curves are: z=4x2+y2     and     x=ey

Q: Find a vector equation and parametric equations in t for the line through the point and parallel to…

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Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar 3v - 4w.

A: we have been given three vectors u = 2i - 5j, v = -3i + 7j, and w = -i - 6j we have to find  3v -…

Q: write the equation of the plane passingthrough P with direction vectors u and v in (a) vector form…

A: P=(0,0,0) , u=212 and v=-321we have to find the equation of the plane passing through P with…

Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Find the specified vector or scalar l-l-2ul.

A: Here given as u = 2i - 5j, v = -3i + 7j, and w = -i - 6j. Thus -2u=-2·2i+2·5j=-4i+10j

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.