Given that p and r find in column vector form:

Q: Prove Ảx (B x Č) = B(Ả C) – Č(Ã B) is true by expanding Ả, B, and components (or Cartesian…

A:

Q: Find the unit vector in the direction of v and verify that it has length 1.

A:

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: Find the vector with the given length || v || = 3, and in the direction of u = (0,2,1, -1)

A: Sol

Q: C A

A: We use Triangle law

Q: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

Q: Find the unit vector in the direction of v and verify that it has length. v = ⟨−6.2, 3.4⟩

A: Now magnitude is,

Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: A. Find the values of a such that vectors and are orthogonal .

A: According to bartleby expert policy only one individual question is to be answered. Kindly repost…

Q: Show that, û . ûm = 0, Use only the fact that û,is a unit vector. Interpret this result.

A: Here we need to prove that dot product of a unit vector and its derivative is zero. Here we use the…

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

A:

Q: For AABC, let b and c denote the vector AB and AC , respectively. The vector BH is orthogonal to AC.…

A: Orthonormal vectors are perpendicular to each other.

Q: [:] [] Find c so that the vectors and are parallel.

A: Find c so that the vectors c4 and 25  are parallel. Let u=c4 and v= 25 be two vectors. Two vectors…

Q: Find a non-zero vector B' which is perpendicular to A'= 2i'-3j'.

A:

Q: Show which of the following are orthogonal vectors v, = 18] V2 = %3D Or = Liel Uz = 18

A: Check the dot product of given vectors are zero or not, if zero the orthogonal otherwise not

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Determine the length of each vector.

A:

Q: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

Q: Find the given vector : Vector of length 3 in the direction of v = 4i + 3j

A:

Q: A vector of 2 unit length parallel to vector 2i + 2j+k is:

A: We know a vector consists of magnitude and direction as we have to find the direction parallel to…

Q: snip

A: We know that two vectors u and v are said to be orthogonal if their dot product u . v = 0. Given…

Q: Show that Il all = 11b|l Are the vectors ã' and b equal?

A: ||a|| = ||b|| a and b are not equal.

Q: Find a vector v parallel to u=4i−3k and with magnitude ||v||=4

A:

Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

A:

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: 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: Are the vectors v = 6i - 3j and w = i + 2j orthogonal?

A: Two vectors are considered to be orthogonal if their dot product is zero.

Q: Find the unit vector in the direction of v = (3, −1, 2), and verify that this vector has length 1.

A: Vector v = (3, −1, 2) Such that,

Q: For any vector v in ℝ3, explain why v × v = 0.

A: Given v∈R3 v×v=0

Q: Find a so that the vectors V=i-aj and w=2i+3j are orthogonal

A: Two vectors V and W are said to be orthogonal if their dot product is 0.    V.W = 0

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A: Explanation: Given that,  Vectors v and w length is 3 angle between vectors v and w:…

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: 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: Find the length of the vector.v = (0, 1)

A: If Vector V = (V1,V2, V3) then the length of Vector ||V|| = (V1)2+(V2)2+(V3)2

Q: Find three mutually orthogonal unit vectors in ℝ3 besides ±i, ±j, and ±k.

A: Vector: At first we can take a=<1,1,1> The second case we can take b=<0,1,-1> The…

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A:

Q: -) THREE VECTORS A, B, AND C ARE RELATED AS FOLLOWS ! A AT 180°, A +C =-5+j15, 2 C = CONJU GATE OF…

A: Solution :-

Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to…

A: Let the two vectors be u=u1i+u2j+u3kv=v1i+v2j+v3k

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

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

Q: . Prove: If a and b are both unit vectors, then axb is a unit vector only when a and b are…

A: since you have asked multiple questions in a single request, we would be answering only the first…

Q: Show that if A⋅(B×C)=0, the three vectors must lie in the same plane.

A: We have to show that if A ⋅ (B × C) = 0 then all three vectors A , B , and C lies in the same plane.…

Q: Given that u =, and z = What is the x component of the resultant vector w = Зи + 22

A: Given: u=4,-5z=-11,-10

Q: Find scalars s and t so that LU = A.

A: Given: A=2611, L=20t-2 and U=130s. To find scalars s and t so that LU=A. Solution: Finding LU.…

Q: Given nonzero vectors u, v, and w, use dot product and crossproduct notation, as appropriate, to…

A: It is known that the unit vector along the direction v is given by vv. Since it is an unit vector,…

Q: Find a nonzero column vector u such that Cu = 4u.

A:

Q: Find a vector B for which that is parallel to A =-6i +3j –2k but has the opposite direction.

A:

Q: One of the following vectors lies in span{ 2+ x +x², 3+x – 2x? } (A) 3 + 2x + 4x² (B) 3 + 2x + 5x?…

A: We have to find

Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.