2. Given that A(- 1, 0, – 3), B(1, – 2, – 2) and C(4, – 2, 1) are three points in the 3-dimensional coordinate system with O as the origin. (a) Find BA · BC and hence find ZABC. (b) Find the vector projection of BC onto BA. (c) Find two vectors which have magnitude equal to 6 and are perpendicular to both BA and BC. (d) Find the volume of the tetrahedron OABC.

Q: 2. (a) Calculate the position vector for P₁ and the displacement vector from P₁ to P₂, where P₁:…

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Q: bäi The cross product of the vectors 3ax + 4ay – 5az and -ax + ay - 2az * ,is -3ax+11ay-7az O -3ax +…

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Q: Consider the points K (−1, 0, 7) and M(1, −2, 5), the vector MN = (1, 4, −3), and the line  I with…

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Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find b.…

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Q: 17. 17. Choose the vector orthogonal to the plane through the following three points P.Q and R. 다음 세…

A: Given three points P(7,-2,0), Q(3,1,3) and R(4,-4,2)  We have to find vector orthogonal to the plane…

Q: Consider the following graph. 6- (4, 4) (4, 4) (1, 2) 2 | (3. 2 3 5 2. 3. (1, 2) 3 4 5 6 -1- 5- (a)…

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Q: A, B, and C are 3 distinct points with non-zero position vectors a, b, and e respectively. a If a x…

A: Given three distinct points are A, B, C. with position vectors a, b, c respectively.…

Q: Г10] Let ÿ = 7 and i = -2. Write y as the sum of two orthogonal vectors, j1 parallel to u and j,…

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Q: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T in the 3D space, figure out c) e1 × e3

A: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T to Find e1 × e3

Q: Given the points M[0.1, -0.2, -0. 1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (a) the vector…

A: This question can be solved using the concept of finding the vector joining two points and dot…

Q: Given the point D(−4, 5, 3) and A = yax + (x + z)z ay, express the D and A in: Kindly answer in…

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Q: 35. The position vectors of the points A and B are OA =2i + j- 4k,OB =-2i +4 j – 2k , a vector…

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Q: Suppose we have the triangle with vertices P(1,5, 1), Q(-4, 10, –1), and R(6, –3, -1). Answer the…

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Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

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Q: Given vector U= ⟨1,-1⟩ and V=⟨1,1⟩, find a linear combination of the vectors u and v of the form aU…

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Q: Find the vector projection of C = ⟨2, −6, −1⟩ onto D = ⟨3, 5, −4⟩ and hence write C as the sum of a…

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Q: 2 Describe each of the translations shown using column vectors. a d e 3 Using the vectors in…

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Q: Write the projection of 2î +3j-k along the vector î+j.

A: Given that: 2i+3j-k along the vector i+j.

Q: 4. Given the two vectors rA =-ax - 3ay - 4az and re= 2ax + 2ay + 2 az and point C (1, 2, 3) find: a)…

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Q: Consider the following graph. (4, 4) 2 (1, 2) 1 3 (a) Find the component form of the vector v. (v,,…

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Q: Given the vectors: A = 7+7+ k and B= 47+ 27+ k Find the vector projection of A onto B: Proj. _, A

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Q: Given the points A(-2, 3, 1), B(0, 0, 2), and C(-1, 5, -2) Express the vector v = (3,2,7) as a sum…

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Q: Given a vector à = 3a, + 2a, – 6as , determine the vector component of à tangential to the cone. O…

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Q: 2. Let each of the vector A = -8a, + 2ay – 4a,, B = 3ax – 4ay |3D Z> + 5a,, and C = 4ax + 5a, extend…

A: Using position vectors of given points. we ca find side vectors of triangle. using magnitude of a…

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: Consider the following graph. (5, 5) 5 y 3 (1, 2) 1. 1 3 4 5 (a) Find the component form of the…

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Q: The z-coordinate of the terminal point of the vector v=-5i-19k whose initial point is (-1,-4,-5) is

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Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

Q: The plane that contains the point (3, –1, -4) and the line with equation y – 1= 3z is orthogonal to…

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Q: Consider the following graph. (4, 5) (1, 3) 1. (a) Find the component form of the vector v. (V, V2)…

A: Given a graph showing the vector.

Q: Question 3. (a) Prove that the planes 4x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b)…

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Q: o find the image of v and the preimage of w. , 2vq – v2 ), v = (1, 1), w = (-7/7, 2, -20) age of v…

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Q: 22. Given that the vectors a = 3i-4j-4k, b = 2i-j + 3k, and c = 4i-3j +5k. The %3D %3D projection…

A: Here let d= a+b d= a + b⇒d = 5 i -5j -kProjection length of vector d = (a+b) on c is given by |d|…

Q: Given a point P: (0,1,2) and the = Gl,0,1> equation p and is pependiculerto and i -L2,3,0>. for the…

A: To find an equation of the plane that contains a point P0,1,2 and whose normal vector is…

Q: If a line is parallel to the vector 4i + 1j + 4k and passes through the point P = (3, 7,9), then the…

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Q: 1. Use the vectors in the figure at the right to graph each of the following vectors on the plane…

A: Draw the correct vectors 2v & -3w than form the triangle sum.

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: Given: a = (-1,-2,2),b=(3,3,4). Find the vector projection of b onto a.

A: Vector projection on b onto a

Q: -) Find the vector form F(t) = ro + tu of the line through the points P(2, 7, 5) and Q(7,8, 12) Find…

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Q: 4. Find the resultant using (a) the head-to-tail method, and (b) by summing up components. For the…

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Q: Given a vector Á = 3a, + 2a, + 6as , determine the vector component of Á perpendicular to the…

A: Topic:- vector

Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k,…

A: (a) To show that triangle ABC is a right angled triangle, use scalar product of vector, that is…

Q: 4. Identify the component form of the vector that maps AABC to its image AA'B'C' A . 2 B. C. 2 A4…

A: Observe the given figure to identify the coordinates of both A, B, C and A', B', C'. x coordinate…

Q: Given a vector à = 3a, + 2a, + 6as , determine a vector that is perpendicular to A and tangential to…

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Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: Given the points P(4, 4, 3), P(1, 4,0) and P3(10,0, 2). Find the vector that is orthogonal…

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Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

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Q: Consider the vectors 1 3 5 2 = %3D 6. 9. Prove that it is not possible to write b as a linear…

A: given u→=122 , v→=306 , w→=3-26,b→=549 to prove- b→ cannot be written as a linear combination of…

Q: 6. Show that the points A, B and C with position vectors d = 32 – 4) – 4k, b = 2î – ĵ + k and & = î…

A: To show that the points A,B and C with a given position vectors forms a right angled triangle.

Q: 1) Suppose a and b are two vectors that start from the same initial point. If |a| = 8 and |b| = 11,…

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