4. If the position vectors of the three points A, B and C are (2, 4, -1), (1, 2, -3) and (3, 1, 2) respectively. Find a vector perpendicular to the plane ABC.

Q: a= b=

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Q: he points A(1,-2,4) and B(2,-4,1) cach make direction vectors with the point (Xo.Yo, Zo). The point…

A: The Parametric equations of the line are the components of the vector equation , and have the form…

Q: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

Q: 2. Given a line that passes through the point (-2,1,3) and is parallel to the line joining A(1,5,3)…

A:

Q: Define the points P = (-4, 6) and Q = (2, 4). Find the position vector corresponding to På. %3D %3D…

A: We will find the position vector of PQ as following

Q: 5. Determine a vector equation of the line that passes through the origin and is parallel to the…

A: Determine a vector equation of the line that passes through the origin and is parallel to the line…

Q: Which of the following vectors is/not perpendicular to the line whose direction vector is (2,-3,5)?…

A:

Q: B) Use vectors to check whether the points A (1,-1,0), B (2,1,-1), and C (-1,1,2), are vertices of a…

A:

Q: 1. Find the equation of the plane. the points. Don't use three (1,2,1), (2,6,3), (0, 1,-1) which…

A: 1:  2: Note: We have taken d as common and taken  it to the other side of the equation.

Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

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Q: Give the vector equation of the plane passing through P, Q, and R. P = (8, 8, 8), Q = (4, 0, 2), R =…

A: The answer is given below:

Q: Draw position vector OP = (-2,-4,3) on the axis below.

A:

Q: 3. A plane contains A(1, -3, 2), B(-2, 4, 2) and C(3, 2, 1). (a) Determine the vector equation of…

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Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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Q: The vector from the origin to point A is given as 4x-4y, and the unit vector directed fron the…

A: Please post the second question separately.

Q: A line passes through points A(-1,-5, 9) and B(8, 5, - 15). A vector equation for the line is 7=(-1,…

A:

Q: (It may help to draw a picture for this question). Let A, B, C be three points with position vectors…

A: