Consider the points P(-1,4,0) and Q(-1,-1,1). a. Find PQ and state your answer in two forms: (a, b, c) and ai + bj+ ck. b. Find the magnitude of PQ. c. Find two unit vectors parallel to PQ.

Q: Determine the angle between the given vectors. (а) а — 3і — 2ј, b %3 2i + 2j

A: a→=3i - 2jb→=2i + 2j

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 14j as…

A: ANSWER IS GIVEN BELOW.

Q: The following diagram shows the parallelogram ABCD. B A D Let AB =p and AC=q. Find each of the…

A:

Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i +j and i- 6j as…

A: Here we have to find the length of the diagonal.

Q: Find the value of a so that vectors U = ai + 3j and V = 9i + 9j are perpendicular. a =

A: Given: U=ai+3jV=9i+9jθ=90ο

Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction?…

A: Given: v=6,9 and point -6,-9 in the same direction

Q: In the figure here, D is the midpoint of side AB of triangle ABC, and E is one-third of the way…

A: Consider the figure shown belowAssume , D is the midpoint of side AB of triangle ABC , and E is…

Q: Given initial point  P1 = (−2, 1)  and terminal point  P2 = (5, 4),  write the vector v in terms…

A:

Q: Find the area of the parallelogram that has the vectors u and v as adjacent sides, where ||u|| = 2,…

A: The area of the parallelogram is ∥u∥×∥v∥×sinθ=2×12×sinπ3=24×32=123   Here θ= the angle between u and…

Q: If u = 5i - j+ k, v =j - 5k, w = -15i + 3j - 3k. Which vectors, if any, are (a) perpendicular? (b)…

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Q: Let 0 be the angle between vectors A and B, find the value of the angle 0 when -6V3A × B = 18Ã. Ē

A:

Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction?…

A: Given: v=6,9 and point in the same direction -24,-27

Q: Given the vector u = (- 5, - 6), find the magnitude and angle in which the vector points (measured…

A:

Q: Consider the following points P and Q. a. Find PQ and state your answer in two forms: (a, b, c) and…

A: We have given two points P0,0,2 and Q-2,4,0.

Q: For what value of (a) will the vectors V=-4i-8j+ak, U=2i+4j-5k are parallel?

A:

Q: Find the value of a so that vectors U = ai + 9j and V 3i + 12j are perpendicular. %D a =

A: Since, We know that Two Vectors are perpendicular to each other if and only if their dot product is…

Q: Find the value of b so that vectors U = 5i +12j and V = 4i + bj are perpendicular.

A: Given :          U=5i+12jV=4i+bj

Q: Obthe resulting parallelogram from the following two vectors that form non-parallel sides A = 3 + 2…

A:

Q: Show that the points with position vectors 3i−5j, 4i+j, 6i+13j are collinear. If the point whose…

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Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction?  (2,…

A: Let the 2 nonzero vectors be v and w and also the scalar vector be λ . Both the vectors are said to…

Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction? (12,…

A: Solution:Given     v=(6,9)To find the vector are parellel to v and point in the same direction.

Q: Given the vector u→=⟨-4,-6⟩, find the magnitude and angle in which the vector points (measured…

A:

Q: If à = 2a, + 2a,y – a, and B = 3a, + 2a, – 6a, are vectors, find (a) Ả ·Ē (b) Ả × B (c) Angle…

A:

Q: Consider the points P(2,7) and Q(6, 4). Write PQ as a product of its magnitude and a unit vector in…

A: Given points are P(2, 7) and Q(6, 4).

Q: Suppose a • b = -12 and b is a unit vector. a Explain why a and b are not perpendicular. b Given…

A:

Q: Find the angle between the vectors v and w v = (2, 1, 3)T , w = (6, 3, 9)T

A: We need to find the angle between the two vectors.

Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction?…

A: Given: The vectors v=6,9, To determine: Whether the vector -24,-36 is parallel to given vector or…

Q: For what values of c are the vectors and perpendicular?

A: we will use dot product of two vector.

Q: Let the vectors a=[1,1,0] b=[3,2,1], and c=[1,0,2]. Find the angle between а) а, b b) b, с с) а+с,…

A:

Q: Given perpendicular vectors a = (5,3,-1) and 6=(2,2,k), find ||||.

A: Given perpendicular vectors a→=5, 3, -1,     b→=2, 2, k   To Find: b→

Q: Calculate the values of a and b so that points A (1,1,1), B( a,2,b) and C(1.0,0) are aligned…

A: If two vector are collinear , then they are scalar multiple of each other. that is AB→=λAC let a ,…

Q: Determine the angle between the two vectors: x = ai+bj+ck and y = di+ej+k where a = 2, b = 5, c = 1,…

A:

Q: Given the points A: (-6,6,-5) and B: (3,-1,0), find the vector i AB i = <

A: Since, we have been given the points A (-6,-6, 5) and B(3,-1, 0).Our Aim is to find the vector u⇀…

Q: Q1.If à = 2a, + 2a, – a, and B = 3ax + 2a, – 6a, are vectors, find (a) Ả · B (b) Ả× B (c) Angle…

A:

Q: 3. Calculate the angle (degrees), between vectors p = 2i +9j – 4k and q = -3i + 5j + 6k correct to…

A:

Q: Given initial point  P1 = (−7, 4)  and terminal point  P2 = (9, 6),  write the vector v in terms…

A:

Q: ) If m = 2i+2j-k and n = 31-6j+2k, find: a) m ·n and b) the angle between m and n. c) the component…

A:

Q: |미350, | w|= 12, 0=35° A) B) W W

A:

Q: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: Let →a=⟨−2,−1⟩ and b→=⟨0,-5⟩. Find the angle between the vector, in degrees.

A: We can find the angle between the vectors as below.

Q: Consider V=(6, -3) & W=(-4, 8) Find angle between the two vectors.

A: Recall: Angle between two vectors:     Let a→ and b→ be two vectors then,             cosθ=…

Q: For what values of b are the vectors (–88, 6, 7) and (b, b², b) orthogonal? Answer (separate with…

A:

Q: Given initial point  P1 = (2, 5) and terminal point P2 = (−1, 6),write the vector v in terms of i…

A:

Q: Given the three vectors A = 3ix + 2iy – İz B = 3ix - 4iy – 5iz C= ix - İy + İz Find the following:…

A: We have to find the vector

Q: Find the equation of the perpendicular bisector of the line join- ing the points with position…

A: From the given information we can draw this figure

Q: The angle that the x-axis make with the plane containing the following two vectors is A = 4â – 3 B =…

A: To find the angle

Q: Find the value of a in the vector i = (a, b) if b = 48 and ||ū|| = 50 %3D v is in Quadrant I

A:

Q: Calculate the slope m of the following vectors and / or line segments in a plane (can be complex) a)…

A: Topic - slope of vector and line Note : As per bartleby guidelines,we are supposed to answer only…

Q: Given the triangle with vertices A=(1,2,3), B=(3,-1,0), and C=(4,1,2), find unit vector of BM, i.e.…

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Q: write the vector v in terms of i and j whose magnitude lvl and direction angle θ are given as lvl =…

A:

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.