16. Consider this regular octagon. If AB =ü and BC =v, express each vector in terms of u and v. B C A H a) GE b) AH с) CD d) OF

Q: Given vector u = (3, 1) and v (1,3) , determine the value of 2u – 3v in component form.

A: Use component wise addition and multiplication for required answer.

Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

Q: Give a vector description of the midpoint M of a line segment AB.

A: According to the vector midpoint formula: Where 'c' is the midpoint position vector of vector 'a'…

Q: If A = 6i + 7j – 10k, B = – 4i + 5j + 6k, C = 10, and C is perpendicular to both A and B, write the…

A:

Q: In triangle ABC a line is drawn from A to the midpoint of BC, labelled D. Prove that vectors…

A: The solution is given by using triangle law of vectors as follows

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: Consider the two vectors A = A,i + Ayj and B = B,î + Byj. In cross product, %3D %3D ixî = j xj = 0,…

A: We have given two vectors A→=Axi^+Ayj^  and  B→=Bxi^+Byj^ i^×i^=j^×j^=0i^×j^=k^, j^×i^=-k^   Find…

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: 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: Given three vectors, u, v, and w, if u (v x w) = 0, what geometrical result can be concluded?

A: We have to conclude the result of u→.(v→×w)=0→.

Q: / If A(1,23=1), B(3)6-7), C(233,-3),D(34-3), Cal culate the angle between the vector Projection of…

A: If vector a→ is projected on vector b→ the the formula of vector projection will be…

Q: Given vector u = (6, –1) and v = (2, –2) , determine the value of u – 2v in component form.

A: Given query is to find the indicated vector.

Q: Prove that two vectors v = (a, b) and w = (c, d)are perpendicularif and only if ac + bd = 0

A: We prove the above statement using the concept of dot product or scalar product of two vectors. The…

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: Is it true that if vectors a-b and a+b are orthogonal, then la|=|b|.

A: Given vectors a-b and a+b are orthogonal. The objective is to prove if vectors a-b and a+b are…

Q: Under what conditions are the following true for vectors u and v in R2 or R3? (a) llu +vll = llull +…

A:

Q: If A=(rsinOcosð,-cos2OsinD, tan, Inr) at P(7,0.08 rad,4.66 rad), determine the vector component of A…

A: Given:

Q: . Given two vectors = w a = a2 show that

A: Given w→ = w1w2w3a→ = a1a2a3 We know that the cross product of w→ and a→ is w→×a→ = ijkw1w2w3a1a2a3=…

Q: Triangles in Space

A: Area of triangle formed by P,Q,R is given by  Area=PQ ⇀×PR⇀2 UNIT VECTOR is given by  unit vector=PQ…

Q: Let C and D be points with position vectors c and d respectively. If |c| = 5, \d| = 7 and c·d = 4,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: Let u be a unit vector in Rn (i.e., uTu = 1) and let H = I − 2uuT . Show that H is an involution.

A: Given : u is a unit vector in Rn.H=I-2uuT

Q: 2. Which polygon is the translation of polygon 1 by: (a) vector AB? (b) vector BC? 2 В 3 4 A C

A: topic - polygons

Q: 2. Find the unique unit vector that bisects the angle between ī = 31 + 43 and w = 51 – 127.

A: The angle bisector is determined by the formula,

Q: e) Four non-coplanar points A, B, C, D are positioned such that the line AB is perpendicular to CD,…

A:

Q: Show that if v and w lie in the yz-plane, then v × w is a multipleof i.

A: Both vectors v and w lie in the y-z plane, which means they must have zero magnitude component along…

Q: Prove that ? is parallel to vector ? using scaler product if ⃗̂̂ ?=−3?̂+4?̂−? ,?=−9?̂+12?̂−3?

A:

Q: If v = 2i + 4j and w = -2i + 6j, find the vector projection of v onto w.

A: Given vectors are: v = 2i + 4j w = -2i + 6j The formula for the vector projection of v onto w is…

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: 16. Consider this regular octagon. If AB =d and BC =v, express each %3D vector in terms of u and v.…

A: Considering OD on x-axis. Angle at center O made by any side of regular octagon is 45degrees.

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

A:

Q: Is the following statement correct? If A, B, C, and D are distinct nonzero vectors represented by…

A: A, B, C, and D are distinct nonzero vectors represented by arrows from the origin to the points A,…

Q: In Exercises 15–18, a. Find the area of the triangle determined by the points P, Q, and R. b. Find a…

A: We'll answer the first question since the exact one wasn't specified . Please submit a new question…

Q: Let v = ai + bj. Show that v/lvl is a unit vector in the direction of v.

A: Consider the following vector: v→=ai^+bj^ Magnitude of vector v→: v→=a2+b2…

Q: Let a=ci+ja=ci+j and b=9i+45jb=9i+45j. Find c so that a and b are orthogonal.

A:

Q: If r is equal to 300 mm, Find: 1.) Rectangular form of r in ft 2.) Unit vector of r

A:

Q: Answer the fellowing muitiple-chorce awestion below algybra A9. w and V are par pandicular vectors…

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: Show that if u+v and u – v are orthogonal, then the vectors u and v must have the same length. If 0…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: Which polygon is the result of reflecting polygon 1 through AB, then translating the reflected…

A:

Q: the angles between the vectors u = 2i - 2j+ k, v = 3i + 4k = O 84.2 O 40.2 O 48.2 80.3

A:

Q: Let a, b, c be distinct non- negative numbers. If the vectors ai + aj + ck, i + k and ci + cj + bk…

A: Introduction :

Q: 3- Given a vector A (r 17.5, 0= 90°, o = 55") and vector B (r=17.5, 0= 40°, q = 55") the distance…

A:

Q: Find the signed volume of the slanted box in R" generated by the vectors 27 11 3 vi = 6. V3 = ,V4 =…

A: Given that, v1=0263,v2=-2-1-10,v3=-1-203,v4=-13-20

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

A: Proceed as shown below...

Q: Show that LM = 2AB.

A:

Q: If v = ai bj is a unit vector, then a? + b² = 1. %3D %3D O True O False

A: v=ai+bj

Q: Under what conditions are the following true for vectors u and v in IR2 or IR3? (a) ||u + v|| =…

A:

Q: If the vectors in the figure satisfy Ju| = |v| = 1 and u + v + w = 0, what is |w|? u |w| =

A: