Let Q be a point in R°. Consider a line passing through P with direction vector d. What is the distance from Q to the line?

Q: nd the length of the vector fo raight line joining the points 5,2). Also find the angle made

A: Given, The vector is formed by the straight line joining the points 1,3 and5,2. The length is to be…

Q: If f(x, y) = 2x² + 5y? and u is the unit vector in the direction of , which of the following…

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Q: Give a vector description of the midpoint M of a line segment AB.

A: According to the vector midpoint formula: Where 'c' is the midpoint position vector of vector 'a'…

Q: Find the value of A which is defined as the angle between i+j and j+ k.

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Q: Given the points P(-3, 4) and Q(-1, 5), express the vector PQ in terms of i and j.

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Q: a) Find the vector that is parallel to the tanget to the circle x2 +y? = 100 at the point (3,4).

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Q: Show that RS is parallel to PQ. P M Q

A: We need to show that RS is parallel to PQ Given that PR= QS , sides are equal The line MN makes and…

Q: If WX is not parallel to UV, what is mZW? W 133° U V mZW =

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Q: If the position vectors of the points A, B, C, D are a = i + j + k, b = 2i + 3j, c = 3i + 5j − 2k, d…

A: Consider the vectors: a=i+j+k……1b=2i+3j……2c=3i+5j-2k……3d=k-j……4

Q: For what value of m, the vector 4i + 2j – 3k and mi – j+ V3 k have same magnitude? Q.3

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Q: Find u · v where 0 is the angle between u and v and ||u|| = 4, ||v|| = 12, 0 = 3

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Q: Construct a copy of the line segment below. ald U V

A: Note : As per out guidelines we are suppose to answer only one question. Since you have asked…

Q: The curve with vector equation r(t) = t'i + 2tj+ 3tk is %3D a line.

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Q: The position vector of a point P is defined as the distance between the origin and the point P.…

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Q: Given the points T (5, 20°, 120°) to P (2, 80°, 30°): find the unit vector in cartesian coordinates…

A: The relation between the Cartesian point (x,y,z) and spherical point (r,θ,ϕ) is x=rsinϕcosθ,…

Q: is parallel to V , and u w is perpendicular to v

A: Given three vectors u=(2,1,-1), v=(-4,4α+β,2), w= (α,0, 3β) To find the values of unknown provided…

Q: 5. For the vector OP = (1,4,-2), determine the direction cosine and the corresponding direction…

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Q: Find u v, where 0 is the angle between u and v. ||u|| = 70, ||v || = 200, e =

A: We have to evaluate u.v  Using formula U.V =||U|| ||V|| cos (theta)

Q: Given u = and v = , sketch u - 2v and identify the direction (from standard position a.k.a. (+)…

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Q: Find u · v, where 0 is the angle between u and v. ||u|| = 4, ||v|| = 14, 0 = - 3

A: This problem can be solved by directly putting given values in the formula for the dot (or scalar)…

Q: find an equation for the line through P perpendicular to v. Then draw a sketch of the​ line,…

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Q: find the length and direction (when defined) ofu * v and v * u. u = 2i + 3j, v = -i + j

A: Given: u=2i+3j, v=-i+j we know that cross product of given two vectors p→=ai+bj+ck, q→=xi+yj+zk is…

Q: Evaluate ry dr +r dy, where C is the positively oriented triangle enclosed by the lines y = I=0 and…

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Q: Let L be the line 8x + 2 in R?. Find vectors a and b so that v a + tb with t ER is also a correct…

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Q: If the position vectors of the points A, B, C, D are a = i +j+k, b = 2i+ 3j, c = 3i+ 5j – 2k, d= k –…

A: The position vectors of points A, B, C and D are a=i+j+k,  b=2i+3j,  c=3i+5j-2k  &  d=k-j. Now…

Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c by establishing that the slope…

A: We first have to find the slope of the given vector and the line. If the slopes are equal then they…

Q: For what value of t , if any, is the vector (4t, -1) parallel to the vector (4, -1) ? OAt=1 OB. t= 2…

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Q: Given ZV = 15, What is the distance from ZW %3D

A: Here ZV=15; we have to find the ZW =?

Q: If å is a vector in the direction of S60°E, then draw its opposite vector and state the direction

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Q: Let C and D be points with position vectors c and d respectively. If |c| = 5, \d| = 7 and c·d = 4,…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 3. if the position function vector r = ti +6tj , find the direction of the vector at time 1 sec جد…

A: The position function vector is,  r=t3i + 6tj To determine the direction of the vector at time t = 1…

Q: Consider the graph provided find the length of the vectors u and i

A: Solution and Explanation is given below....

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i, v = -3j

A: Given vectors: u=2i+0j+0k and v=0i-3j+0k u×v=ijk2000-30u×v=i0×0-0×-3-j2×0-0×0+k2×-3-0×0u×v=-6k The…

Q: a) Find the vector that is parallel to the tanget to the circle x2 + y2 = 100 at the point (3,-4).…

A: a) Given equation of circle, x2 + y2 = 100. We have to find the vector equation which is parallel to…

Q: If u and v are orthogonal, what is the magnitude of u × v?

A: We define the cross product of any two vectors as :                            |u×v|=|u||v|sinθ…

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: Given that the position vectors of points T and S are 4a, + 6a, – a̟ and 10a, + 12a, + 8a,…

A: This question is related to vectors.  We will solve it using given information.

Q: Show that w is in span(B) and find the coordinates of w with respect to B. B = 6.

A: Linear Algebra

Q: Let Q be a point in R. Consider a line passing through P with direction vector d.What is the…

A: Let Q be a point in ℝ3. A line L passes through point P with direction vector d→

Q: w, and z head to tail as needed to sketch the indicated vector. 3 w

A: NOTE: Refresh your page if you can't see any equations. . here the height of the triangle is x=4…

Q: find the length and direction (when defined) ofu * v and v * u. u = i + j - k, v = 0

A: Consider the given vectors and rewrite vector v in terms of i, j and k. u=i+j-kv=0v=0i+0j+0kTo find…

Q: A line L has a direction vector v = i+ 3j+ V6k and passes through the point Q. Find the distance…

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Q: Let Q be a point in R°. Consider a line passing through P with direction vector d.What is the…

A: We are asked to find the distance from a point Q in ℝ3 to the line which passes through a point P…

Q: and Let ū Let e be the angle between ū and ū. ob tuse ? why ? acute, right , or ca) Is (6) Find a…

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Q: Consider the lines 3 - z x – 5 l1 : 2 and I. Find two unit vectors that are parallel to l1.

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Q: Given the x and y components, describe the resultant vector. Round magnitude to the nearest tenth…

A: We’ll answer the first question (Q.no. 7) since the exact one wasn’t specified. Please submit a new…

Q: For vectors v and w E R, show that: (a) |u x v||? = ||u||2 ||v||2 – (u - v)2 (b) ||u x v|| =…

A: derive a formula for the magnitude of v×u, for nonzero vectors v,u:…

Q: Draw a diagram to illustrate point R divides line PQ such that PR=RQ and R is the midpoint of PQ,…

A: Concept: Vector: A vector is a -dimensional entity with significance and course. A vector may be…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.