8*. Suppose that a vector in R° has a head at (2,-3,6) and a tail at (5,3,4). Write this vector in standard notation. Then draw the vector in standard notation in R 7 and c = 9. Let a 4 (a) Compute a, 3a, and -2a, and draw each vector in the same xy-plane. |(b) Compute a plane (but a different one from the one you drew for (a). How are the vectors a -b and b - a -b, -b, and b - a, and draw the vectors a, b, a b, a - b, and b - a in the same xy- a related? (c) Compute -2c and 3a - 2c, and draw the vectors a, c, 3a, -2c, and 3a - 2c in the same xy-plane (but a different one from the one you drew for (a) and (b))

Q: In 3-D, let L be a line that does not pass through the origin. let v1, v2, and v3 be three vector…

A: We have to decide there vectors v1, v2, v3 are linearly indipendent in R3 or not.

Q: Determine k so that the vectors (1, –1, k – 1), (2, k, –4), (0, 2, + k, – 8) in R³ linearly…

A:

Q: Compute the orthogonal projection of 7 = proj,(v) = 4 [1] onto the line L through -4 and the origin.

A: Given:    Data is given

Q: 27 Let L be the line in R³ that consists of all scalar multiples of the vector 2 Find the reflection…

A:

Q: 14. Given the vector form of a line in three-space to be [x, y, z] = [2,6, – 3] + t[4,10,6], find b.…

A:

Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

A: Cross product

Q: Suppose and are non-zero, parallel vectors. Which of the following could not possibly be true?

A:

Q: Consider the following graph. 6- (4, 4) (4, 4) (1, 2) 2 | (3. 2 3 5 2. 3. (1, 2) 3 4 5 6 -1- 5- (a)…

A:

Q: If the vectors a=(2,5,-1) and b3(3,-3,k) are orthogonal, the the value of k is

A: Given : a = 2,5,-1b = 3,-3,k

Q: Г10] Let ÿ = 7 and i = -2. Write y as the sum of two orthogonal vectors, j1 parallel to u and j,…

A:

Q: Suppose vị and v2 are vectors with |v1| = 2, |v2l = 3, and vị · v2 = 5. Let v3 = proj,, v2, V4 =…

A:

Q: التاريخ 5.1 1 1 If the vector [42] An with the straight Piecel the end point?

A:

Q: Find a vector that has the same direction as 8i-j+4K but has a length of 6

A:

Q: Let A = (-3, 4), B = (-2, b), C = (1, 6), and D = (a, 2). Then AB and DC are opposite sides of the…

A:

Q: Determine if i = (1,0.-4) and w=(9,3,1) are parallel vectors.

A: Use the vector product to show the given vectors are parallel.

Q: Define the points P(-4, 1), Q(3, -4), and R(2, 6).

A: The given points are The vector QP is So, the unit vector (v) of QP is

Q: Show that direction vectors of the lines 3 L: and

A: We have to find the direction vectors for the lines L1: x-32=y+14=z-2-1 and L2: x-35=y+1-2=z-32.

Q: 4. Find the vector equations for the line of intersection of the following planes: 2x – y – 5z = -14…

A:

Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

A:

Q: 4

A: We are given the following vectors.

Q: Express the vector from P(-1, -4, 6) to Q(1, 3, -6) as a position vector in terms of i, j, and k.

A: Given vectors are P-1,-4,6 and Q1,3,-6.

Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

A:

Q: Show that the vectors 1 – t,1+ 2t² , t² +t+1, t² + 2tare linearly dependent and indicate how one of…

A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

Q: If vectorAB =-7i + 3j + 8k and A is the point (-2, -3, 6), find B.

A: Given : AB =-7i + 3j + 8k and A=(-2, -3, 6)

Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

A:

Q: - Show that the vectors X, - () 5e3t and X2 = ) 2et 7et form a linearly independent set.

A:

Q: Suppose that u, ū, and w are vectors in R3 such that ūxi = (2,7, 3) and ūxu = (-5, 4,0). Find: 1.…

A:

Q: Suppose that the sum of the three vectors u, v, and w shown in the figure is the zero vector. If…

A:

Q: -11 and ỹ = Express the vector u as a linear combination of x 28 x+ y.

A:

Q: Sketch the vector b = <3, 4> based at P = (−2, −1).

A: Sketch the vector b=<3, 4> based at P=(−2, −1).

Q: photo is attached

A: Given informationVector V = (-3, 5)

Q: When V is spanned by {v1, v2, . . . , vk} and one of these vectors can be written as a linear…

A:

Q: 2. Sketch the vector v = 4i – 6j. 1아 6 4 2- 10 -8 -6 -4-2 2. 4. 6 8 10 -2 -4 -8 C0 10

A:

Q: if vector AB =(-7i+3j+8k) and the point A= (-2,-2,6) find B

A: Given, AB =(-7i+3j+8k) and the point A= (-2,-2,6) Let the coordinates of B be (x,y,z) Now, AB = B-A…

Q: 2. Find the cross products of the vectors in the diagram above.

A: The concepts to be used: (i) The components of vectors can be written in terms of cosine and sine.…

Q: Find the vector ž, which is perpendicular to vectors å = (2,3, –1) and 5 = (1,–2,3) and satisfies…

A:

Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: Let å = (- 5, 5, – 3) and b = (4, – 1, 0). Find a unit vector which is orthogonal to å and b and has…

A: Given query is to find the unit vector orthogonal to a and b

Q: If the vectors a=(2,5,-1) and b=(3,-3,k) are orthogonal, the the value of k is

A: Given : a = 2,5,-1b = 3,-3,k

Q: 1 Consider the line through the vector a = Find the project of b = (1,2,3) onto this line.

A:

Q: If ï = (, 2), find a vector i that is perpendicular to ū.

A:

Q: 4 2. Decide whether the vectors (1, 2,0,-1], [2, 6, -3, -3], [3, 10, -6,-5] are linearly…

A: Given vectors are ,  [ 1,2,0,-1 ] ,  [ 2,6,-3,-3 ] ,  [ 3 ,10 ,-6 ,-5 ]  (.)  The given vectors are…

Q: 3. If a = 3x - 5y and b=-2x+9y, write the vector 5a-8b in terms of x and y

A:

Q: Consider the lines L1 and L2 in R³ given by the vector equations L1 :ở = (2,4, 4) + t(4, 1, 5) and…

A: Given: L1 : v→ =2 , 4, 4+t 4, 1, 5 And  L2 : v→ =1, -3, 2+t -2, 3, 1

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

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

Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

A: Given: x1=2i+j, x2=6i+3j we know that for any given vector v=ai+bj, length l of vector is given by…

Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

A:

Q: Find the equation of the plane in xyz-space through the point P=(3,3,2) and perpendicular to the…

A: topic - equation of a plane

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Let us consider a line l joining by  two points A  and B. Consider a point P (not on line l ) then…

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.