Let P be a plane in space and let v be a vector. The vector projection of v onto the plane P, projpv, can be defined informally as follows: Suppose the sun is shining so that its rays are normal to the plane P. Then projpv is the "shadow" of v onto P. If P is the plane x + 2y + 6z = 6 and v = i+j+k, find projpv.

Q: Find a vector equation of a plane having x-intercept 4, y-intercept -1, and a z-intercept of 5.…

A: The x-intercept is 4. The y-intercept is -1. The z-intercept is 5.

Q: {(0, 1,-1), (1,2, ).( 3,-1,4)}

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Q: Consider the points P(2,4,3) and Q (1, –5,2) in 3- space. Find the position vectors rī and rz for P…

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Q: Find a direction vector for the line containing the origin (0, 0, 0) and the point (2, 3, – 1).

A: The given points are 0,0,0  and  2,3,-1

Q: Describe the Z-axis in R as the span of a vector. Can you describe it as the span of other vectors…

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Q: Find the equation of the plane sanned by the above two vectors

A: Given: Two vectors u=223 and v=-20-3. To find: Equation of plane spanned by given vectors.

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: 4. If the position vectors of the three points A, B and C are (2, 4, -1), (1, 2, -3) and (3, 1, 2)…

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Q: t a = (3,3) and b = (4,1) draw and label the vectors a, b, -a and b - a on a set of coordinate axes.

A: Given vectors a=(3, 4) and b=(4, 1)

Q: Let X and Y be points in R³. Let P be a point on the line segment joining X and Y such that the…

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Q: Find the vector expression for the line that is the intersection of the planes 3x−3y−2z=−2 and…

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Q: Consider a plane with direction vectors  [−2,8,5] and  [5,0,−7]. The plane passes through the point…

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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 =…

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Q: Let b = 4i + 3j and c be two %3D vectors perpendicular to each other in the xy-plane. All vectors in…

A: Given: b→=4i+3j and c→ are two vectors perpendicular to each other in xy-plane.  To find: All the…

Q: Find the vector A having Ray (PQ) as a representation where P = (3, 7) and Q = (5, 4). Draw Ray (PQ)…

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Q: Suppose vectors u and v lie in the xy-plane (the z-component of each vector is zero). Now suppose…

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Q: onsider the points (1, 2,- 1) and (2, 0, 3). a. Find a vector equation of the line through these…

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Q: Let b = 4i + 3j and c be two vectors perpendicular to each other in the xy-plane. All vectors in the…

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