Consider the points A(-3, 4, 2) and B (8,-1, 5). (a) (i) Find AB. () Find AB (ii) 2 1 A line L has vector equation = 0+1 -2 -5 2 (b) (i) Find the value of y. 8 (ii) Show that AC-10 Find the angle between AB and AC. Find the area of triangle ABC. (c) (d) The point C (5, y, 1) lies on line L.

Q: Given the point A(2,1,-3) and B(6,-1,-5) write the vector equation and the parametric equations of…

A: Once we get vector form of the equation we can easily write the parametric form of equation of line.

Q: (e) Find the angle between two vectors u = (4, -3, 6) and v = (3, 0, 1).

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Q: The unit vector of the PQ (of point P(-3, 4, 1) and terminal point Q(-5, 2, 2)). - The angle between…

A: here we have

Q: Given three points P(2, −2, 1), Q(3, −1, 2), R(3, −1, 1). (a) Find the area of the triangle…

A: given: three points P(2, −2, 1), Q(3, −1, 2), R(3, −1, 1) (a) we have to find the area of the…

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Find the solution of sin² (x) – 4sin (x) – 1 = 0 for all angles between 0 and 2n.

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

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: If a point A, the position vector ai + bj lies on the line L, vector equations r = 2i +5j +c(i-i),…

A: To find the value of (a), we need to ensure that the position vector of point A, (ai + bj), lies on…

Q: (9, - 플이 2

A: Given, the  point (r, θ, z)=(9, -π2, 8).

Q: v = {3,k,-2} and w = {-2,1,2k} What value(s) of k are the vectors v and w perpendicular?

A: To determine the value of k for which the vectors v and w are perpendicular.v=3, k, -2 and w=-2, 1,…

Q: Let be two vectors, such that a=(3î+2j-2k) cm and b=(2î+2ƒ+k) cm, calculate: (A) C²=3(a¹·b¹)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: 3. (7-9) A vector has an initial point at (1, –1) and an endpoint at (8, 6). Write the vector in…

A: The given start and endpoints of vector are (1,-1) and (8,6) We know that the magnitude of a vector…

Q: Consider the points P = (1,1) and Q=(3,-1). (a) Draw the points P and Q and draw an arrow from P to…

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Q: rite the equation of the line passing through P with direction vector d in vector form and…

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Q: perpendicular to (x, y, z) = (1, -2,0) + r(1, -1, 1) through P(1, 3,5) [parametric equations]

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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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