Let a = 2i + j - 2k and b = i+j. If c is a vector such that a.c = |cl, |c – al = 2v2 and the angle between (a x b) and c is 30°, then |(a x b) × c| = %3D %3D

Q: Consider three vectors u = 3i +j+ ak, = 2i + bj +k, = -4i + (b – 2)3 + (b+ 8)k, where a and b are…

A: The solution are next step

Q: If v = 2i - 5j and w = i - j, find the vector projection of v onto w.

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: If u is a unit vector and a is a positive scalar satisfying au + = 0, find a and u.

A: If u is a vector and a is positive scalar satisfying   au+1,-2,5=0.  To find : a and u.

Q: Consider the points A(1,-5), B(-1,3) and K(4,-2) in 2D. A. Determine the vector AB B. Determine the…

A:

Q: Let A and B be nonzero vectors. Find k e R such that A – kB is orthogonal to A + B.

A: We know if a vector P→ is orthogonal to another vector Q→ then scalar product (dot product) is zero.…

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: 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: The vector result of (ì − 2j +3k) · (−2ī + 2j − 2k) is a. -i + 7j b. -i+j-k d. j+7k e. -i+7k c.…

A:

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+k %3D %3D %3D where a = 2, b…

A:

Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 & w=12+-12=2

Q: Decompose the vector v=3i+2j into two vectors v1 and v2, where v1 is parallel to w=2i+j, and v2 is…

A: Decompose v into two vectors v1 and v2,where v1 is parallel to w and v2 is orthogonal to w.v=3i+2j,…

Q: Let E 3a, + 4a, and F 4а, — 10а, + 5а.. %3D %3D (a) Find the component of E along F. (b) Determine a…

A:

Q: For any vector u, v E R³, v. (uxu) (uxu) = 0.

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: A vector orthogonal to both u = 2i + j – 2k and v = -j+k is اخترأحد الخيارات -i – 2j + 4k .A | i –…

A:

Q: The length of the vector u = (0, 1, 1) is:   a)  1 b)  2 c)  √2 d)  3 e)  √3

A: We have to find

Q: Decompose v into two vectors,one parallel to w and the other orthogonal to w. v = 2i + j; w =4i + 3j

A: we have to decompose v into two vectors, one parallel to w and the other orthogonal to w. v = 2i +…

Q: Given the points C(-4, –5) and D(-1, 1), express the vector CD in terms of i and j.

A:

Q: Find a vector perpendicular to each of the given vector a = ßi +j+k ,b = 4i + aj – k. %3D |

A: Applying cross product we have

Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

A:

Q: 2. Let Ā and B be nonzero vectors. Find k e R such that B – kĀ is orthogonal to Ā – B.

A:

Q: Decompose v into two vectors v, and v2, where v, is parallel to w and v, is orthogonal to w. v = 2i…

A:

Q: 14. Find a vector perpendicular to both of the vectors * (ũ + v) and (ũ – v) where ủ = 2i – j + k,…

A:

Q: W 2-Find a vector that is perpendicular to both B = i +j-k B = 4i – j 1. A = 2i +7j – 4k | > 2. A…

A:

Q: Let a = 3i – 6j + 4k and b = 2i + j – 2k. a Find c, the vector component of a perpendicular to b. b…

A: Given, a=3i-6j+4k and b=2i+j-2k

Q: If a = i+ 2j + k and b = i+ 5j +k, find a unit vector with positive first coordinate orthogonal to…

A: Given that     a = i+2j+k and b = i+5j+k We have to find a unit vector with positive first…

Q: Let v and be two nonzero vectors in R' and 0 be the angle between 4. (" and . If and are linearly…

A: Given query is to find the angle between vectors when they are linearly dependent.

Q: If the vectors u and v are linearly independent with au + bv = 0 then a = b = 0 O a = 0 and b # 0 0…

A:

Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

Q: 4. ABP is a triangle, M is a point on AP. AB = a, AM = 26, and MP = b. N is the midpoint of BP. C is…

A: Follow the steps.

Q: Let c, (t) = e'i + 7 sin(t)j + t*k and c2(t) = e-Sti + 3 cos(t)j – 41*k. (Enter your solution as a…

A: Solved below

Q: ..) Find a vector ğ so that if F{f} = (co, C, C2, C3) then Ff ® ğ = (co, 0, 3c2, 0). %3D 160

A: The objective is to find the vector g so that is F(f)=(c0,c1,c2,c3) Then, Ff⊙g=(c0,0,3c2,0) It is…

Q: Consider the vectors y= 3i + 4j + 5k and w= i + j + k. Express the given vector in terms of i, j and…

A: The given vectors v=3i+4j+5k and w=i+j+k

Q: If A is a conutant vector and R= 3xi+ 3yj+ 32K, then grad (3A -R) = ? %3D A O 3A ©9A 27 A

A: A is a constant vector  R=3xi+3yj+3zk 3AR=9Axi+9Ayj+9Azk To find grad(3AR) Let Φ=9Ax+9Ay+9Az gradΦ=i…

Q: Find u x v for the given vectors. u = i -2j +3k, v = -2i +2j +3 k u x v = ai +bj +ck where a=], b=],…

A:

Q: The vector v, where |v|= 28, is in the direction of the vector 2i + 3j – 6k. v = 25. A 14i + 21j –…

A:

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

A: Topic:- vector

Q: Given the points A(-6, 4) and B(-3, 5), express | the vector AB in terms of i and j.

A:

Q: If a = i+ 8j + k and b = i+ 13j + k, find a unit vector with positive first coordinate orthogonal to…

A:

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

A:

Q: Suppose that A= 2i + j, B= i – 4j + k, and Ĉ =j+k. What is the direction of vector A? A A. 26.6 E of…

A:

Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v+ w.

A:

Q: For any vectors U, V and scalars a, b, prove that (aU) x (6V) = ab(U × V) (a) (b) (aU) - (bV) = ab(U…

A:

Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v + w.

A:

Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

Q: Given v = 6i + 2j and w =i-j, a. Find projwv. b. Decompose v into two vectors v, and V2, where v, is…

A:

Q: If a = i+ 4j + k and b = i + 8j + k, find a unit vector with positive first coordinate orthogonal to…

A: Given : a=i+4j+k and b=i+8j+k.

Q: If v = 5i + 6j and w = 10i + 12j, find proj,v. Then decompose v into two vectors v, and v2, where v,…

A: