Q: Given three points in space P(1, -1, 0), Q(2, 1, -1),and R(-1, 1, 2), do the following: 1-Find the normal vector to the plane that contains all the three points. 2-Find the scalar product of PQ and PR and the angle 0 between them. 3-Show that |PQ x PR| = |PQ||PR| sin 0. 4-Prove that the area of a triangle PQR is PQ x PR|.

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Q: unit vectors inclined to each P = a cost cos 2t+b sint cos 2t + c sin two non-collinear dicular to…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Orthogonal component of AP →=AP⇀sinθ we know AB⇀×AP⇀= AB⇀AP⇀sinθ

Q: Similarities

A: (As per bartleby guidelines, for questions containing multiple subparts, only first three subparts…

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Q: Find the sine of the angle between vectors u = (-3, 2,6) and v = (3,2,6) by using the cross-product.

A: Given: The vectors u =(-3, 2, 6) and v=(3,2,6) Find : The sine of the angle between the vectors u…

Q: Use the method above to find the distance from the point P(-3,1,7) to the line through A(1,1,0) and…

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Q: Find a unit vector with positive first coordinate that is orthogonal to the plane through the points…

A: Given that the points P-2,-3,-1 Q3,2,4andR3,2,7  .

Q: 1. Consider the vectors ữ = (-1,–1), ở= (1,2) and w (3, a). (a) Find the resultant of ū and ū. (b)…

A: As your question contains multiple subpart. I am solved the first 3 subpart. please repost other as…

Q: Find the angle between the vectors v and w v = (2,−3)T , w = (3, 2)T

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Q: d 6

A: 5. In the given right triangle , the hypotenuse is 41 and the perpendicular length is 40. Apply the…

Q: 2. The four points P(3, 1, 2), Q(1,0, 2), R(2, 1,0) and T(1, 1,-2) in R' lie on the same plane. (a)…

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Q: (2.) Let V be the vector space of M1x2(C) over R. (a.) Give a basis for V. (b.) Let W = { { 1] z €R.…

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Q: All v's, w's, i's, and j's are vectors) Let v =⟨2,4⟩ and w =⟨3,−5⟩ (a) Find a vector of unit length…

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Q: For the vectors x=(1, -1, i, -i) and y=(1, i, -1, i) find the span(x,y)

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Q: L is a line in 2-space or 3-space that passes through the points A a then the distance from a point…

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