Example 4: Find the equation of the plane through the point (-4, 3, 1) that is perpendicular to the vector a = -4 i+7j-2 k. Solution:

Q: If a = i +9j+k and b = i +19j+ k, find a unit vector with positive first coordinate orthogonal to…

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Q: Find the equation for the plane through the points Po(-3,5,3), Qo(0, – 5,2), and Ro(1,1,- 2). The…

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Q: A city is described parametrically by the equation r = (ai + bj+ck) + svi + tv₂ where v₁ = 3i+j+ k…

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Q: Find the equation of the plane containing the points (1,1,−2),(1,2,1),(−1,2,−2)

A: The equation of plane containing the points 1,1,-2, 1,2,1, and -1,2,-2 is to be evaluated.

Q: Three points (9,-2, 4), (5,-5,3), and (7,1,-3) can be the vertices of a triangle. If you can make…

A: Vectors

Q: Find an equation of the plane through the three points P = (0, 0, 4), Q = (-3, 4, 0), R = (-1, -2,…

A: The given problem is to find the equation of plane passing through the given 3 points P(0,0,4),…

Q: Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c.

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Q: Calculate the sum of the vectors that can be drawn as a vecto from the vertices of the triangle…

A: The vertices of the triangle is A7,4,-4, B1,-1,1 and C-8,-1,3

Q: a = 2 ,8 ,2 ,−2 ,−4 ,−3 ,−11, −4 ,9 ,7 and b = 8,−1 . SOLVE Ax =b for x , and write x in…

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