The three vertices of a triangle are located at A(6,-1,2), B(-2,3,-4), area of the triangle; (c) a unit vector perpendicular to the plane in whic Ans. 24a, + 78a, + 20a,; 42; 0.286a, + 0.928a, + 0.238a,

Q: Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: 4. Use vector methods to find (a) the area of the triangle ABC where A(-2, -1, 1), B(3,-2, 1) and…

A: (a) Given vertices of the triangle are A(-2,-1,1) , B(3,-2,1) and C(1,3,-2)

Q: Find equations for the planes The plane through A(1, -2, 1) perpendicular to the vector from the…

A: The normal vector of the plane is given by A(1,-2,1)  The point of passing is (0,0,0). The equation…

Q: What is the terminal point of the vector a = <1, 3> based at P = (2, 2)? Sketch a and the…

A: Consider the provided information, The component vector v=PQ→ where P=a1,b1 and Q=a2,b2 are…

Q: Find the angle between two vectors ū = (1, –1,0), and ở = (2, –1,2) %3D

A:

Q: Find a unit vector perpen dicular to the plane of the vectors a = (2, -3,1) and b = (1, 2, -4)

A:

Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

A:

Q: Use the vectors u = (1,-3,5) and v=(2,1,-3) to Find 1 the area of the parallelogram determined by u…

A:

Q: Find two unit vectors that are normal to the plane determined by the points A (0, –1, 2),B (1,…

A: To find the two-unit vectors that are normal to the plane determine by the given points.

Q: Prove using vectors that the points (1,1,2)A(2,1,1), B(1,2,1), C represent the vertices of a…

A:

Q: Find a vector that is orthogonal to the triangle with vertices P=(1,0,0), Q= (0,2,0), R=(1,1,1)

A: RECALL: Orthogonal vector:  Let us consider to vectors a→ and b→ then , cross product of a→ and b→…

Q: Find the unit vector orthogonal to the plane through the points P ( 12, 3, -4 ), Q (-1, -2, 2), and…

A:

Q: Determine whether the vectors a = (1,2,3),b = (1,3,1),c =(2,2,2) plane? coplanar, that is, they lie…

A: Answer and explanation is given below...

Q: Find the area of the parallelogram that has the vectors as adjacent sides. u- (3, -5, 3) v = (2, 0,…

A:

Q: prove using vectors that the points (0),2 -2- (B2,0, -2, C, (2,2-,10) represent the vertices of a…

A: We have to check weather the given points are Vertices of Traingle or not.  After that we have to…

Q: The unit vectors normal to the vectors (2, - 8,11) and (- 3,0,5) are

A: Find unit vector

Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: A unit cube (whose length, width, and height are 1 unit each) with a vertex at the origin lies in…

A: Given, cube is-

Q: Find a unit vector that is perpendicular to both ủ = (2,1, 2) and v = (2,– 2,– 1).

A: Given, u→=2,1,2 and v→=2,-2,-1 we are asked the unit vector that is perpendicular to both.

Q: Find the angle θ between the vectors.u = (1, 1, 1), v = (2, 1, −1)

A: The vectors are To find the angle between the given vectors, use formula

Q: Find the angle θ between the two vectors.u = (0, 4, 0, −1), v = (1, 1, 3, −3)

A:

Q: Find the equation of the plane containing the point ( – 5, – 10, 9) and the two vectors and -

A: Given that , Plane containing the point -5,-10,9 So , a→=-5 i^-10 j^+9 k^ And vectors are ,…

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (3, 2, −1), v = (1, 2,…

A: Now,

Q: Find a vector V of a magnitude equals 14 and perpendicular To the plane in space which includes the…

A: Explanation of the answer is as follows

Q: Find the angle θ between the vectors.u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

A: The given vectors are, u = (1, −1, 0, 1), v = (−1, 2, −1, 0)

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)…

A:

Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

A:

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are the vertices of a…

A:

Q: Find the angle θ between the two vectors.u = (10, −5, 15), v = (−2, 1, −3)

A: The given vectors are To find the angle between the given vectors, use the formula

Q: Find the equation of the plane containing the points P = (−1, 3, 2),Q = (−5, 1, 1), and R = (6, 0,…

A: Given,             The plane containing the points P = (−1, 3, 2), Q = (−5, 1, 1) andR = (6, 0, −3).

Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

A: From the given points we can find two vectors and after that, using the fact that if one vector is…

Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

A:

Q: Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,–4) and R(6,–2,-5) is…

A:

Q: Find a unit vector which is perpendicular to both đ = (1, 1, 0) and b = (-2, 3, 0) Answer:

A:

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = (2, −1, 0), v = (−1,…

A:

Q: Find the angle θ between the vectors.u = (3, 4), v = (5, −12), ⟨u, v⟩ = u ∙ v

A: Given vector: Formula used : By dot product equation:

Q: ind two unit vectors that are normal to the plane determined by the points A (0, -1, 3),B (2,-1,-2),…

A:

Q: Find the angle θ between the vectors.u = (0, 1, 0, 1), v = (3, 3, 3, 3)

A:

Q: Two vectors are given as A=-1a, + 6a, + 6a, B=-6a, + 5a, + 6a, Find a unit vector normal to the…

A: Given,Two vectors are-A=-1ax+6ay+6azB=-6ax+5ay+6az

Q: Find a unit vector that is perpendicular to both ū = (1, 2, –2) and v = (2,1,2). Answer:

A: The vector which is perpendicular to the plane containing vectors u and v can be calculated by the…

Q: Determine two unit vectors, vand wl, perpendicular to the plane passing through the z-axis and point…

A:

Q: Find the angle θ between the vectors.u = (2, 3, 1), v = (−3, 2, 0)

A: Given: u=2,3,1, v=-3,2,0 we know that angle θ between two given vectors A=x1i+y1j+z1k, B=x2i+y2j+z2k…

Q: Let the vectors (2,3) and (-6,4) be    Your point product is: ? The angle between the vectors is:…

A:

Q: Find the area of the parallelogram that has the vectors u (2,-1, 3) and v (4, -5, 1) as adjacent…

A: As this is a multiple question according to the Bartleby Answering rule, only first question is to…

Q: By finding the dot product for each pair of vectors determine if they are perpendicular: (1,2) and…

A:

Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

A:

Q: Determine the dot product of the vectors а 3 (-3,—2, 3), b %3D (2,1,-2). b = (2,1,–2). a = 1. а:b —…

A: Solve for dot product

Q: 1. Prove using vectors that the points (-1, 3, 3), (0, 1, 2), (2, 2, 2), and (3, 0, 1) are the…

A: as per the rule we are authorized to provide the answer for only one question so please provide…

Q: Find an equation of a plane passing through the given point and perpendicular to the given vector.…

A: The equation of the plane perpendicular to the vector <a, b, c> is: ax+by+cz+d=0 Therefore,…