All small squares in the picture have side length 1. C a) Find a vector equal to KG + GD™ b) Find a vector equal to AB -2JD c) What is the sum AB +BG¯ +GF* + FA ? M

Q: If the volume of the parallelepiped determined by the vectors A = i +ak, B = 8i-5j + ak and C = 2i…

A: Given vectors are A = i + αkB = 8i - 5j + αkC = 2i + 3j - 8k

Q: 3) Write a two column proof. Given: ABCD is a parallelogram AABD = ACDB Prove:

A: We can prove the same as below.

Q: ABCD is a quadrilateral with AB equal and parallel to DC. Prove that AD is equal and parallel to BC.

A: Given: ABCD is a quadrilateral where AB=DC and AB parallel to DC. Prove: AD=BC and AD parallel to…

Q: The volume of the parallelepiped determined by the vectors a =,b = and c = is: (A) 12 (B) 6 (C) 24…

A: The given vectors are a→=3,4,5, b→=2,1,-1 and c→=3,2,1

Q: The volume of the parallelepiped determined by the vectors à =,b = and c= is: (A) 12 (B) 6 (C) 24…

A:

Q: Find the area of triangle with the vectors p(0,1,4),0(-5,9,2) and R(7,2,8) А: 30 B: 40 С:35 D:45

A: Given: Vertices of triangle          P0,1,4O-5,9,2R7,2,8…

Q: Find the Euclidean inner product of the given vectors. 3 4 u = v = (u, v) = Ex: 5

A:

Q: If A : li + 4j – 8k, B = -6i + 5j + 6k, C 9, and C is perpendicular to both A and B, write the C in…

A: Given, A→=i^+4j^-8k^B→=-6i^+5j^+6k^ Let, the required C→ vector be, C→=c1i^+c2j^+c3k^.......(1)

Q: What is the cross product of the vectorS 2i + 3j + k and 61 + 9j + 3k? Explain why your answer is…

A: Cross Product: Cross product of two vectors is the method of multiplication of two vectors. A cross…

Q: Use the accompanying figure to write each vector listed in Exer- cises 7 and 8 as a linear…

A: Given - Use the accompanying figure to write each vector listed in Exercise 8 as a linear…

Q: If the volume of the parallelepiped determined by the vectors ä, 5, č e R³ is A cubic units, which…

A: Consider the provided question, a→∧3b→∧b→∧c→Let a→∧3b→=u→a→∧3b→∧b→∧c→=u→∧b→∧c→…

Q: Find all values of h such that the vectors {a,, az} span R?, where a1 a2

A: Given that,

Q: Find the dot product of the following vectors u and 7.

A:

Q: Use the polygon law of addition to draw the resultant vector ( å + b) + ở for the following yectors.

A: The given vectors are added

Q: (d) Let u, v, w be arbitrary vectors in R³. What does the set of all combinations, Cu + c2v + C3w,…

A:

Q: Determine the value(s) of k such that the area of the parallelogram formed by the vectors a = (k +…

A:

Q: What is the angle between the vectors u = and v = ? 213° O 188° O 111° 120°

A: Solution:

Q: If the volume of the parallelepiped determined by the vectors A = i + ak, B = 8i - 5j + ak and C =…

A:

Q: Create a two-column proof. B A D Given: Rhombus ABCD with diagonals AC and BD intersecting at point…

A: Properties of the Rhombus -  Rhombus has four equal sides and opposite sides are parallel.…

Q: The volume of the parallelepiped determined by the vectors a =,b = and = is: (A) 12 (B) (C) 24 (D)…

A: Volume of parallelopiped

Q: a) Show that the three vectors A = 2i – j+ k , B = i - 3j – 5k, Č =-3î + 4j + 4k %3D form the sides…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: In Exercises 30–35 compute the indicated quantities when u = (−3, 1, −4), v = (2, 0, 5), and w =( 1,…

A: Given: u = (−3, 1, −4), v = (2, 0, 5), and w =( 1, 3, 13)

Q: 2. Which polygon is the translation of polygon 1 by: (a) vector AB? (b) vector BC? EN B 3 4 nob C…

A: Given:

Q: Prove the property if a and b are vectors and m is a real number.a . b = b . a

A: Proof : let a and b are vectors and m is real number. To prove :   a . b= b . a

Q: In the diagram, ABC is an equilateral triangle, and D, E and F are the midpoints of its sides. As a…

A:

Q: In kite ABCD, LBAC = 62° and LBCD = 52°. Find the measure of LABC. %3D %3D B.

A: In kite ABCD, ∠BAC=62° and ∠BCD=52°.To find the measure of ∠ABC.

Q: Find the sum of the vectors and illustrate the sum geometrically.u = (−1, 4), v = (4, −3)

A: Given Data The first vector is u= (-1, 4). The second vector is v= (4, 3).   The expression for the…

Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

A:

Q: Find the area of the parallelogram determined by the given vectors. 3 u = 2i – j+ 3k, v = ÷i + 2j –…

A: If vector a and vector b are the two adjacent sides of a parallelogram then the area of the…

Q: Find the area of the parallelogram with vectors a = 3p+ 2q, b= 2p-qwhere \pl = 4, lq] = 3, (p, q)…

A: To find the area of the parallelogram with the vectors a=3p+2q,b=2p-q where p=4,q=3,p,q=3π4.

Q: Find three nonzero vectors a, b, and c such that a × b = a × c = 0but b = c.

A: Find nonzero vectors a, b ,c such that a×b=a×c=0 but b≠c. If two vectors are parallel then their…

Q: Prove that if A and B are any nonzero vectors and C: lBlA + lAlB, then the angle between A and C has…

A: Let us determine the angles between the vectors using scalar product of two vectors in the next…

Q: Let ABCD be a trapezoid with parallel sides AB and DC. Suppose that the length of AB is 20…

A: Two lines which never intersects each other are considered parallel lines. And the distance between…

Q: Find the area of the triangle with two sides given by the vectors a = i – j+ 4k, and b = 2i – 4j+1k

A:

Q: 18. Show by vector methods that the median (a median joins the vertex of a triangle to the midpoint…

A:

Q: If the volume of the parallelepiped determined by the vectors d, b, čeR' is a cubic units, which of…

A: Given, 2a→∧b→∧b→∧c→ Let, 2a→∧b→=u→ Now simplifying the given equation by apply the vector dot…

Q: O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

A: Our are objectives to check which vectors are parallel and which vectors are perpendicular

Q: In the adjoining figure, ABCD is a trapezium in which AD//BC. M and N are mid points of diagonals BD…

A: Given that ABCD is a trapezium in which AD||BC. Also M and N are the midpoints of the diagonals BD…

Q: In Figure , A, B, C, D,E , and F are the vertices of a regular hexagon centered at the origin.…

A: Given that, OA→=aOB→=b

Q: G エ

A: Here is your answer starts.

Q: The vertices of quadrilateral ABCD are given as A(0, 3, 5). B(3, – 1, 17), C(7, –3, 15), and D(4, 1,…

A:

Q: 8. In triangle ABC, the point D is the midpoint of BC and E the midpoint of AC Vectors are marked as…

A:

Q: 4.15. Given vectors u = and v =, find the projection of u onto v.

A: Proceed as shown below...

Q: express each vector as a product of its length anddirection. 9i - 2j + 6k

A: The given vector is u=9i-2j+6k. Compute the length as follows. u=92+-22+62=81+4+36=81+40=121=11

Q: Assign AB//FG, BD//GI, DE//IJ, EA//JF. and C, H are the intersections of the diagonals of the…

A: Given: Using the scalar product of the three vectors, calculate the volume of a given solid figure.

Q: Prove the property if a and b are vectors and m is a real number.m(a . b) = a . (mb)

A: Let a=a1, a2, a3   and  b=b1, b2, b3. This implies that,