Consider the vectors i = (2, 5, 1) and i= (-2, 4, 3). (a) nitude w| = 8? Give a brief explanation of your answer, and then find one such vector w. How many different vectors w exist which are perpendicular to both ū and i and have mag- (b) Compute the scalar projection of (u – ī) onto (ũ+ ū). The dot product of the vectors (u x T) and (ữ x u) is a negative number. Use the geometric (c) properties of the dot and cross products to explain why this must be true OR verify that it is true by computing (ū x T) · (ỡ × ū).

Q: Let J = 31 +43 - K and ✓ = 2₁ +3₁-2k be of two vectors. Find the component and projection U in the…

A: u→=3i+4j-k,v→=2i+3j-2k

Q: Write N(A) as the span of a vector (r vectors). What is dimN(A)? Why?

A: Null space, N(A) is the set of all vectors x in R^4 here, which are solutions of the equation Ax=0,…

Q: Find the cross products u xv and vxu for the vectors u = = (3,5,0) and v = (0,3, - 6). uxv = (Di+…

A:

Q: Find the projection of the vector a = (2, 5, 1) on the vector b = (1, 1, 3) O a. (10/11)(ax + 3ay +…

A:

Q: Find the magnitude of the vector AB with initial point A(-1, 3) and terminal point B(2, -1). Give…

A: Step 1: Step 2: Step 3: Step 4:

Q: Let u= (2,-3, 2, 5) and v a- i b- = (1, 2, 0, -4). Find scalars a and b so that au + bv = (0, -7,2,…

A:

Q: Find all vectors u such that ux(1,1,1)=(8,-5,-3).

A:

Q: The vector v has initial position P and terminal pet P (2, 5); Q=D (-5,-1) v 7i+ 6j Ov- 6i+ 7j…

A: Let's Solve, Answer: Option D

Q: Show that the vectors are orthogonal.

A: Given vectors are u=<u1, u2>=<4, -1>v=<v1, v2>=<2, 8>

Q: 5) Find a vector in component form that is orthogonal to the vectors a = (9,3,-7) and b = (10,-8,2)

A:

Q: (a) 3u7 u3 (b) (c) u2 (-2u5) (d) 2u2 : (-u5)

A:

Q: ● Let A = (1.-2,4), B (0,3,2), C (-1,4,-2) be three points in R. Find the vectors u-AB and v-AC.

A: Let A=(1, -2,4), B=(0,3,2), C=(-1,4,-2) be three points in R3. We have to find the vectors u and v.

Q: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

A:

Q: Vektor m =[5, -2, 1] Vektor n =[-6,-2, 4] a. find vektor p where p = -2m+0.5n b. find vektor…

A: a) write p in terms of m and n with the given relation p =…

Q: Find the vector v, where u = (-2, 3) and w = (-3, -2). Su + w) Illustrate the specified vector…

A:

Q: The vector -3 (GIE) -1 -4 0 -7 vectors -3 2 belongs to the span of the 5 Select one: O True O False

A: Given: W=span-3-10, -1-4-7. To check v=-325∈W.

Q: Draw the vectors in standard position in R2 with their tails at the point (2, -3).

A:

Q: 7. (a) Let v be a vector with initial point (-1, 4) and terminal point (3, -2). Let w be a vector…

A: