2. P.P, if P, is the point (1, 3) and P, is the point (2, -1). 3. OP, if O is the origin and P, is the midpoint of the vector P,P2 joining P(2, -1) and P2(- 4, 3).

Q: The vector equation for the line segment that joins the point P(1, 3, –2) to the point Q(2, – 1, 3)…

A:

Q: Determine a vector equation for the line that is perpendicular to 7 = (4, 1) + s(−3, 2), sER, and…

A: We need to find the equation of line perpendicular to r→=(4, 1)+s(-3, 2),  s∈ℝ and passing through…

Q: For what values of a and ß will the vector (a, 1, B) be orthogonal to (2, 0, 7) and (-1, 1, 2)? α =…

A:

Q: B) Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis…

A: See the attachment

Q: photo attached

A: Given point can be written in vector form as,

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

A:

Q: (b) Find the angle between the vectors u and v if u = (2,3,5) and v = (1, -4,3) in %3D R3.

A:

Q: Suppose U and W are vectors in R" then ||U +W|| - ||U|| + || W|| if the angle between U&W is equal…

A:

Q: Let a = (2, – 3) and b (0, – 3). - - Find the angle between the vector, in degrees.

A: Given a→=<2,-3>           b→=<0,-3>

Q: Which of the following vectors is perpendicular to the plane 2x - 3y + 5z + 7 = 0?   a. [-3, 2,…

A: Given: The equation of the plane is  2x - 3y + 5z + 7 = 0   To determine: The vector which is…

Q: if vector AB=i+7j-4k and B is the point (9,3,5) find A

A: Let A=ai^+bj^+ck^B=di^+ej^+fk^ be twovectors.Then AB→=d-ai^+e-bj^+l-ck^

Q: α, β and γ are the angles made by the vector with x, y and z axis respectively. The squares of the…

A: Given ,  α, β and γ are the angles made by the vector with x, y and z axisrespectively. We have to…

Q: A vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

A:

Q: Suppose thatu and v are vectors in both of length and that the length of u-v is and the angle…

A: Let's find.

Q: Given that - (1, 2, 3) and - (4. 0, – 4) find the vector where %3!

A: In this question we have to find the vector z.

Q: Given the two points A(1,2,3) and B(2,-3,4) which of the following is the vector equation passing…

A:

Q: Suppose L1 and L2 are disjoint (nonintersecting) nonparallel lines. Is it possible for a nonzero…

A: Given:

Q: If A(1,2.-1) B(3.6-7), c(2,3.-3) D(3.4,-3) Calculate the angle between the vector Projection of ÄB…

A: According to question given that A(1,2,-1)B(3,6,-7)C(2,3,-3)D(3,4,-3)Angle between a pair of lines…

Q: Give the terminal point of the position vector of u= (3,4). Clearly show why your answer is…

A: Given that Position vector of u→=3,4 So, graphically it is as below:

Q: Consider the points A (10, 9) and B (0, – 7). Find the vector AB. АВ

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

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

Q: Given three points P (1, 4, 6), Q (-2, 5, -1)  and R (1,  -1, 1) Find a vector perpendicular to the…

A:

Q: Find vector c = 3u – v, if u = and v =.

A: Given u = 2i - 7j + 3k and             v = 0i + 4j -  k = 4j - k Now vector c = 3u - (1/2)v c = 3(2i…

Q: 03, If a=(3,-1,1), for what value ofe is the vector b-(3,c,-1) perpendicular to a?

A:

Q: Find a vector perpendicular to d = [5,–4,6] and h = [-1,3,9].

A:

Q: Suppose we have the triangle with vertices P(1,6, 1), Q(-3,7,–3), and R(5, 1, 1). Answer the…

A:

Q: If (a,ß.r) is a vector of magnitude 24 and having the same direction as the vector (1,-22,-2), then…

A:

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: 1. Assume the lengths of the vectors 2a – b and å + 35 , assuming å = (2,1,3) and b = (-1,2,2) 2. If…

A: Using scalar multiplication of vectors and magnitude of vector concepts  we can solve this question

Q: Let A = (-5,5,-3), B= (-3,4,3) and P= (k,k,k). The vector from A to B is perpendicular to the vector…

A: Two vectors are perpendicular when the dot product is zero.

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: 13. Given the points A(3,5) and B( – 3, – 7), find a. the vector equation of the line.

A:

Q: Find the vector w which is of length 6 and oppositely directed to u=(2,-2,1) Select one: O None W=…

A: A vector oppositely directed to  u⇀ = <2,-2,1>  is  w = − u = − <2,-2,1>  i.e.  w =…

Q: 2. If A = 2a, + 0.3a, – 1.5a, and B = 10a, + 1.5a, - 7.5a,, Show that A and B are dependent vectors.

A: The solution is given as

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

A:

Q: Find the vector v with the given length and the same direction as u.||v|| = 5, u = (√5, 5, 0)

A: Let the vector u is:   Now, The modulus of vector u is :                                     The…

Q: If the magnitude of the vector u is √2 and its direction is 225°, then its components are:   (1,…

A: Solution of question as follows

Q: The length of the vector c = (2, -3, 1) is %3D

A: Length of vector equal to magnitude of that vector  if v = <x,y,z>  then magnitude/Length =…

Q: Express the vector in the form (V= ai+ bj+ck) *, if A(1,0,3) and B is (-1,4,5):

A: Vector from

Q: For the vectors u = (- 1,3) and v= (-4,2), calculate proj,u and scal,u. proj, u = D

A: Vector and scalar projection

Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa…

A: We have to find the value of lambda by using the data given above

Q: For what values of a and B will the vector (a, 1, B) be orthogonal to (4, 0, 3) and (-1, 1, 2)? a =…

A:

Q: A- If P1(1,3, –2) and P2(4,7,-2) are two points. 1- Compute the length of 2P,P2 2- Is the vector…

A:

Q: Determine if the vectors t= %3D(-16, 24) and s= (3, 2). are orthogonal, parallel, or neither.

A: We have to calculate dot product and magnitude of the given vectors

Q: value

A: If, P, Q & R are collinear, then,  The position vector of QP is, The position vector of P - the…

Q: the vector from P1(1, 3) to P2(4, –2) is

A: Given :

Q: Given that = <1, 2. 3) and - (4. 0. –4) find the vector where -W+37-0

A: