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|.

Q: Find the resultant vector A + B and the resultant angle with respect to positive x-axis where vector…

A: Since vectors are not given so lets understand the concept to add the two vectors. Parallelogram law…

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: Consider the position vectors @ = 1î −3ĵ+2k and b = −1î÷2ĵ– 2 k. (i) Find the lengths of a and b.…

A: The question asks you to find several things related to the position vectors a and b:(i) Find the…

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: Find the distance of point A(2/3, 2) from the line that passes through the origin and parallel to…

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Q: Find the vector equation for the line passing through the points P₁(-3, 6, 8) and P₂(−6, 0, 12). 0 0…

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Q: 1. Find a unit vector perpendicular to the line passing through the points (1, 0, -3) and (2, 1,…

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Q: Let* be the angle between the vectors ₁ and ₂. Let be the angle between the lines l₁ and ₂. We have…

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

A: Distance = 4.41

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

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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: Which of the following is a normal vector to the plane which is parallel to vectors (0,−3,1) and…

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Q: 6) Find two unit vectors that are parallel to the tangent line of f(x) = tan(x) at the point (7,0).

A: Given that f(x)=tanx We have to find two unit vectors that are parallel to the tangent line f(x) at…

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: 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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Q: 1. (a) Calculate the dot product of the two vectors (b*) Find the value for c for which 2 and [2] C…

A: Calculating the dot product of two vectors

Q: (3) Find the angle between the vectors u= 2i-2j4tk and

A: given vectors are  u=2i-2j+k  and v=3i+4k find the angle between these vectors