Q#1 (A) Find the reflection through origin and projection onto , axis of the given vector 3 = (-2,1)

Q: Find both the vector equation and the parametric equations of the line through (0,0,4) in the…

A: Explanation of the answer is as follows

Q: Find parametric equations for the line described below. The line through the point P(-1, -1, 5)…

A: Question 17 In general, we know that the equation of the line passing through the point (x1, y1, z1)…

Q: 6. Find the unit vectors that are parallel to the tangent line to the curve 2x3 at the point (2,…

A: The given curve is y=2x33 at the point 2,163. Calculate the unit vector that are parallel tot he…

Q: Find both the parametric and vector equation of the line segment between (−2, 3) and (5, −1) where 0…

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Q: Find an equation of the plane. the plane through the point (5, 6, 5) and with normal vector 6i + 8j…

A: As we know that the equation of the plane which is passing through a point Px0,y0,z0  and normal…

Q: Determine the vector and parametric equations of the plane containing the point (1, -5, 9) and the…

A: Answer

Q: What is the vector parametric equation L(t) for the line through the points (5,-5,0) and (0,-3,3)?

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Q: (-1,4) onto the Question 2. Calculate the projection of the vector u = vector v = (-4,2). Also draw…

A: Projection of a vector on other vector

Q: (A) Find plane equation that passes through the point (7,3,-5) and contains unit tangent vectors of…

A: To find the equation of a plane containing two lines and passing through a point (a, b, c) is given…

Q: What is equation of the plane passing through the point A(-2,-1,-3) and paralleto the vectors a=3+2k…

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Q: Expreas the unit vector dirccted toward the point (0,0, A) from arbitrary point in the plane --2. an

A: In this question, we have to find the unit vector toward the given point from the given plane the…

Q: 13. Find an equation of the plane through the point (1,2,3) and perpendicular to the vector…

A: Given a point P( x, y, z) and a vector (a, b, c) which is perpendicular to the given plane

Q: (a) Find a vector parallel to the line of intersection of the planes 4x + 3y – 2z = -5 and -5x + y –…

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Q: Find an equation of the plane. The plane through the point (2, 3, 6) and with normal vector 8i + j…

A: We will solve the problem.

Q: Find both the vector equation and the parametric equations of the line through (0,0,0) that is…

A: Given vectors area. u=2,0,2w=-2,-1,0a=0,0,0 Find the vector equation of the line perpendicular to u…

Q: Find an equation of the plane. The plane through the point (2, 9, 6) and with normal vector 7i + j –…

A: Find an equation of the plane

Q: 6. Find the distance of the point (-1,1) to the line given in vector form (x, y) = (2,0) +t(4, 3).

A: Given that: The point is (-1, 1).The vector is:  (x, y)=(2, 0)+t(4, 3)

Q: (a) Find a vector parallel to the line of intersection of the planes -x + 3y + 4z : 0 and -x - 3y –…

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Q: Find a vector tangent to the curve of intersection of the two cyclinders x2 + y? = 8 and y? + 22 = 8…

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Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Two vectors Px1,y1,z1 and Qx2,y2,z2 Line segment P to Q: 1) Parametric form is…

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A: Use the direct formula for equation of plane passes through a point and with given normal vector.

Q: 1. Find both the vector equation and the parametric equations of the line through (−3​,5​,6​)and…

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Q: (1 point) The planes 4x + 4y- z= 10 and 5x + 4y-4z 9 are not parallel, so they must intersect along…

A: The  intersection of two planes is always a line .

Q: example of a vector equation for a line in 3 dimensions which doesn’t intersect the plane at z = 0

A: Given that:a vector equation for a line in 3 dimensions which doesn’t intersect the plane at z = 0

Q: Find Vector, Parametric and Scalar equations for the line that passes through t -2,11) and (6,1).

A: Given: - The line that passes through the points -2,11and 6,1. To find: - The parametric equations…

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 an equation of the plane passing through the point perpendicular to the given vector or line.…

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Q: 3) Find a vector equation and parametric equations for the line segment that joins (-2, 4, 0) to…

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Q: Find the scalar equation for the plane passing through the points P-(-1. 5.-1. P=(-1, 6, 5), and…

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Q: Find an equation of the plane passing through the point perpendicular to the given vector or line.…

A: Given point is (0,4,0) and normal vector is -7i+5j.

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

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Q: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

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Q: Give a vector parametric equation for the line through the point (4,-3) that is perpendicular to the…

A: Give a vector parametric equation for the line through the point (4,-3) that is perpendicular to the…

Q: 4. Determine a vector equation for the plane that is parallel to the xy -plane and passes through…

A: Due to our answering guidelines we can only answer one question at a time, therefore I will be…

Q: 8. Consider the following two planes: one with equation 4x – 5y + z = -2, and the other which passes…

A: Given: Given, equation of the plane, 4x- 5y +Z = -2 The other plane passing through the point (1, 1,…

Q: Find an equation of the plane. The plane through the point (9, 3, 4) and with normal vector 8i + j…

A: To find- equation of  the plane.

Q: Find the vector and parametric equations for the line through the point P= (3,0, –1) and the point Q…

A:

Q: Q3: Find the scalar and vector components of the vector with initial point (2, 1) and terminal point…

A: Given initial point A(2,1) and terminal point B(-5,7)

Q: (a) Find a vector parallel to the line of intersection of the planes 4x – y – 3z = 6 and -5x + 4y –…

A: According to question given thatplanes equation 4x-y-3z=6-5x+4y-4z=3

Q: (2t, 1 – t, 4t) is a parametrization of the line passing through the point (0, 1,0) and also…

A: The statement : <2t, 1-t, 4t> is a parametrization of the line passing through the point (0,…

Q: Find the vector equation of the plane taking into account that 4x - y - z = 3

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Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+y-2z = 3.

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Q: I’ve gotten this far already. I need help finding a non-zero vector that is orthogonal to both…

A: Two vectors are said to be orthogonal to each other if their dot product is zero. we need to find a…

Q: Find parametric equations for the line described below. The line through the point P(1, 1, -2)…

A: Use equation of parametric line and put value

Q: 3. The position vector [3 2 1 1] lies in the YZ plane and forms 30 degree with the principal axis.…

A: Given: Position vector 3211 lies in the YZ plane and forms 30°. To find: On rotation, it forms 45°…

Q: (a) Find a vector parallel to the line of intersection of the -2. 3y - 4z planes -x + 3y + 4z = 0…

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Q: 1.23. Express the unit vector directed toward the point (x, Y, z) from an arbitrary point in the…

A: Express the unit vector directed toward the point (x, y, z) from an arbitrary point in the plane y =…

Q: Represent the line segment from P to Q by a vector-valued function and by a set of parametric…

A: Given information: The points are P(0, 0, 0), Q(5, 2, 2). Calculation: Find the vector valued…

Q: 10. Determine the scalar equation of a plane that is perpendicular to the line: |1,2, 3| + t|-2,4,…

A: A normal of a plane perpendicular to the line will be parallel to the line. So the plane is:…

Q: The line L is parallel to the plane x+y+z=2 and is perpendicular to the vector (-1,1,–2). If the…

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Q: perpendicular

A: