Owing vectors is perpendicular to the line L: 2x +3y- 6 = 0 2i + 3j O 2i - 3j (후 +1를 이 rious

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: Show that v = ai + bj is perpendicular to the line ax+ by = c by establishing that the slope of the…

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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: Show that the lines L1 : x = 4 – t, y = 2t, z = 2+t and L2 : x = 1+ 4t, y = 3 – 8t, z = 5 – 4t are…

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Q: Which of the following vectors is parallel to the line 7x+ 14y = 20? %3D (-6,3) (8,-16) (2,4) 0.…

A: We first find the slope of the line using y=mx+b form

Q: A straight line has vector equation given by r=(1-A)i+(3+2A)j.How far is this line from the origin?

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Q: Is the line x = 9- 8t, y= 4 + 2t, z= - 5t parallel to the plane 2x + y-z=2? Give reasons for your…

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Q: Determine the value of k for which the direction vectors of the lines x+3 Z = y = -1 are…

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Q: If r1,r2 and r3, are three parallel vectors of the same magnitude, Prove that r1+r2+r3 is equally…

A: GIVEN: r1 , r2 , r3 are three parallel vectors

Q: find the length and direction (when defined) ofu * v and v * u. u = 3/2 i - 1/2j + k, v = i + j + 2k

A: Given

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. X = 4t, y = 4 –…

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Q: Show that the lines L1 : x =1– t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y= 3 – 6t, z = 5 – 3t are…

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Q: Find the coordinates of a point P on the line and a vector v parallel to the line. X - 8 y + 2 = z +…

A: This question is based on 3-d coordinate geometry.

Q: What angle does the line of intersection of the planes (x 2y + 3z 5 and 4x+y-2z-7 make with the…

A: The dot product of two vectors u→, v→ is calculated using the formula: u→·v→=u→v→cosθ, where θ is…

Q: A line L has a direction vector v = 2i + 4j + V5k and passes through the point Q %3D Find the…

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Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 5t, y = 9 –…

A: Let's find.

Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

A: Given  AB=i+4j-2k and B is the point (5,1,3)

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: 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: 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: * For the vectors v=16,8) and W=18,6), validate the Schwarz and Triangle mequaiity and fino the…

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Q: In vector form, the equation of a line is given by r = (0, 1, 2) + t(2, 1,0), where t e R. T…

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Q: The plane that contains the point (3, –1, -4) and the line with equation y – 1= 3z is orthogonal to…

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Q: Show that v = ai + bj is perpendicular to the line ax + by = c by establishing that the slope of the…

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Q: I Given that = 10 and y=7 and the angle between and vis. The dot product of the vectors u-v = =…

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Q: Find the area of the parallelogram with vectors a = 3p+ 2q, b= 2p-qwhere \pl = 4, lq] = 3, (p, q)…

A: To find the area of the parallelogram with the vectors a=3p+2q,b=2p-q where p=4,q=3,p,q=3π4.

Q: If is perpendicular to v, then u × v + v O 2|7| II

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Q: 27. Are the points P(1, 2), e(7,3), and R(-2, 1) on the line with vector equation = (19,5) + s(6,1),…

A: According to our terms and conditions I have solved first question for next question repost

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: (a) For the vectors d = (2, p, 8) and b = (q, 4, 12), determine values of p and q so that the…

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Q: For two nonzero vectors u and v, if u v=0 then u and v are parallel.

A: Given that u and v are two nonzero vectors   Dot product of two nonzero vectors u.v=|u|.|v|…

Q: 2. Given two non-parallel lines l1: r = 2+t, y = 4+t, z = 8, and l2: x = 3, y = 2 + t, z = 5+t, (a)…

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Q: The plane that contains the point (3, –1, –4) and the line with equation = y – 1 = 3z is orthogonal…

A: Let:x-02=y-11=z-013=kL: x=2k, y=k+1,  z=k3P1:(3, -1, -4)Put k=0, k=1P2: (0, 1, 0)P3: (2, 2,…

Q: Find the coordinates of a point P on the line and a vector v parallel to the line. x - 8 y + 3 = z +…

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Q: Define the line Lo to be a = xo + at, y = yo + bt, z = z0 + ct. If Lo passes through the origin,…

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Q: Show that A(x - x0) + B( y - y0) = 0 is an equation for the line in the xy-plane through the point…

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Q: Write down the line equation a) given a point Q and a vector v. b) given two points R and Q.

A: Since, our aim is to find the equation of a line that is :-(a) passing through a given point Q and a…

Q: Qre Show that The lines Z+3 w/ parals. are malle! 1-3. 3 %3D 9 3.

A: We know that for a line  By applying above formulae for given lines L1 : x-11=y+32=z+33 then…

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 5 -…

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Q: Show that the indicated diagonal ofthe parallelogram determined by vectors u and v bisects the…

A: The given parallelogram is   Here, we are given |u|=|v| So, u+v is the required diagonal

Q: 3- Given a vector A (r 17.5, 0= 90°, o = 55") and vector B (r=17.5, 0= 40°, q = 55") the distance…

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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: Determine a vector equation of the line passing through (6, 0, 3) and parallel to the line of…

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Q: Let fiz) = x2 + iy? where x and y are the real and imaginary parts, respectively of z and C is 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: Which of the following planes are parallel to the vector (4, 1,-5)? Select one or more: O a. 6x + y…

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Q: For Exercises 17 and 18, find the acute angle between the given lines by using vectors parallel to…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

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…