A line I through the point (5,3, -6) has direction cosines and Find the vector and parametric quations of the line.

Q: Find a vector equation for the line through the point (-3, –1,8) perpendicular to the vectors ū =…

A: vector equation can be find in the following way:-

Q: The unit vector from the origin to the point A is given as (6, -2, -4), and the unit vector from the…

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Q: A vector starts at point ( -3, 3) and ends at point (-1, -5) what is the vertical component of the…

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Q: A vector has initial point (−11,−12) and terminal point (20,−19) The component form of the vector…

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Q: In point P(-6,-8,8), express that vector that extends from P to Q(8, 6, -1) in: a. rectangular…

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Q: What position vector is equal to the vector from (3, 5, -2) to (0, -6, 3)?

A: We have given two vectors;  (3, 5, -2) , (0, -6, 3)

Q: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

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Q: Find a vector equation and parametric equations for the line segment that joins P to Q. P(-4, 8, 0),…

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Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: photo attached

A: Given that a vector V goes from the origin to a point (5, -5).

Q: A plane in R'is perpendicular to the vector (4, 2, – 9), and contains the point (- 9, 5, - 8). Find…

A: A plane in ℝ3 is perpendicular to the vector 4, 2, -9 and contains point -9, 5, -8To find the…

Q: What is the vector between the point (−3a,−7b) and the point (−4a,−5b)?

A: Vector between two points A and B is B-A

Q: Finally, verify that the vectors satisfy the Parallelogram Law |||² + ||||? 3. ī = (2, –1), w =…

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Q: Find vector, parame tric. and symmetric equations of the line containing the point P and paralel to…

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Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: Determine vector and parametric equations for the line through the point (2, 1) and parallel to the…

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Q: Find the symmetric equations of the line that passes through the point (3,6, –10) and is parallel to…

A: The line passes through a point means that the point lies on the line. The direction vector of a…

Q: Find the vector from the origin to the point of intersection of the medians of the triangle whose…

A: To determine the point of intersection of the medians of the triangle.

Q: Given a vector with initial point (−8, 3) and terminal point (5, −5), find an equivalent vector…

A: In the question we have to find an equivalent vector with initial points (0,0).

Q: Find the equation of the plane containing the point ( – 5, – 10, 9) and the two vectors and -

A: Given that , Plane containing the point -5,-10,9 So , a→=-5 i^-10 j^+9 k^ And vectors are ,…

Q: How long is the shadow cast by a 540-foot tower when the sun's rays follow the vector [6,10,-27]?…

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Q: give the equation of the line in vector form, parametric form and symmetric form. k) The line…

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Q: Give a vector parametric equation for the line that passes through the point (–2, 1, –2), parallel…

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Q: Find the scalar equation for each line: (a) a line through the point (-6, 7) with direction vector…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: The vector equation through the point (-2,5,3) and pe O O O

A: Here we have to find the equation of the vector passing through the point (-2,5,3) and normal to…

Q: Find the distance of point 4(2/3,2) from the line that passes through the origin and parallel to the…

A: follow next step

Q: Find the symmetric equation for the line through the point of (2.-5,4)and a vector (3,–1,-3).

A: Given the vector is, 3,-1,-3 And the point is, (2,-5,4). The parametric equation for…

Q: Let vector AB = (2,3,1). If the coordinates of A are (2,1,5), what are the coordinates of the point…

A: Vector AB= B-A

Q: Specify the unit vector extending from origin toward the point G(2,-2,-1). Graph a vector V in the…

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Q: Find the acute angle formed by two diagonals of a cube. (vectors) show complete solution.

A: It has been assumed that the length of each side of the cube is a unit.

Q: Consider the vector whose initial point is P(-6, 6) and terminal point is Q(5, 3). Find the position…

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: A hiker walks 4 km north and then 5 km northeast. Draw displacement vectors representing the hiker's…

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Q: The symmetric equations for the line passing through (-3,–4, -5) and parallel to the vector (1,7,–…

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Q: Find the distance of point 4(2-/3,2) from the line that passes through the origin and parallel to…

A: Distance of a point A(x1, y1) from the line ax+by+c=0 is given by d=ax1+by1+ca2+b2

Q: direction as the vector from the point ?=(0,3) to the point ?=(−2,−2)?

A: Given query is to find indicated vector.

Q: five vectors in Span v1, V2}. Do not make a sketch. 8 - -

A: In this question, the concept of the span of the vector is applied. Span The smallest linear…

Q: Find a direction vector for the line containing the points (-1, 5, 2) and the point (2, 3, - 1).

A: We have to find a direction vector for the line containing the points -1, 5, 2 and 2, 3, -1. We know…

Q: Consider the vector whose initial point is P(-6, 1) and terminal point is Q(-5, -3). Find the…

A: Recall: Position vector v→=a, b where a=x2-x1 , b=y2-y1 We have (x1, y1)=(-6, 1) and (x2, y2)=(-5,…

Q: a) Find vector equation and paramedrie equahion for the line that passes through the point (5,1,3)…

A: The objective is to find the vector equation and parametric equations for the given problem

Q: Find the vector of length 2 making an angle of 45° with the x-axis.

A: Find the vector from the given data

Q: The vector (1, 0, 0) makes a 45 degrees with the vector (x, y, z). What is the relationship between…

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Q: Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set…

A: Represent the line segment from P(−2, −3, 8), Q(5, 1, −2) by a vector-valued function and by a set…

Q: A direction vector passes through a unit cube from the (1/4, 1, 1/4) to the (1, 0, 3/4) positions.…

A: The direction passes through a unit cube from the 14,1,14 to the 1,0,34 positions. We have to find…

Q: Draw two vectors, v and w, with the same initial point. Show the vector projection of v onto w in…

A: Consider two vectors v and w such that the angle between v and w is θ<90°. Now, plot the two…

Q: What is the component form of the vector whose tail is the point (-3, 2) and whose head is the point…

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Q: The vector PQ has initial point P(-5, –6) and position vector (12, 9). What is the terminal point Q?

A: The initial point of the vector PQ→ is  Px1,y1 = P-5,-6 The position vector is  PQ→ = 12,9 To…

Q: Find a unit vector perpendicular to both (3,-2,4) and (-1,2,-3).

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Q: Show that the equation of a straight line in space, represented in the Cartesian basis, is given by…

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Q: In Cartesian coordinates, the position vector at point (3, 40, 1) is represented by 2.29ax+1.93ay+az…

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Q: In Cartesian coordinates, the position vector at point (3, 20, 1) is represented by…

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