he vector v = ai + bj is parallel to the line bx – ay = c. Use this fact to find ector starting at the origin. (4,2), v = - 4i – 2j he equation of the line is (Type an equation.)

Q: Express (-1,2,4) as linear combination of x = (-1,2,0), y = (0,-1,1) and z = (3,-4,2) in the vector…

A: Definition used -                       If we have to write a vector as a linear combination of…

Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Describe the graph of the equation: r = 4ti – 8j + (1 + 2t)k. [Choose the correct answer.] The…

A: It is three dimensional, so each points must have three components (x,y,z).

Q: 2. Let G and H be the points G (4, 5) and H(11, -8). 2a Find the vector HG in component form: HG 4…

A:

Q: Evaluate: if vector OA = (2,3) and OB (-1,-2) Show all steps please

A: if a vector is of the form  a→=a1,a2  then a→=a12+a22 see  below the answer

Q: M] - [8] x+y -3x+y.

A:

Q: Hw.L showthat Vi=3inbj andVz 2-i-zj have opfosite directions.

A:

Q: If a point A, the position vector ai + bj lies on the line L, vector equations r = 2i +5j +c(i-i),…

A: To find the value of (a), we need to ensure that the position vector of point A, (ai + bj), lies on…

Q: Describe the graph of the equation: r = 4ri – 8j + (1 + 2t)k. [Choose the correct answer.]

A:

Q: Find the unit vector in the direction of (5, –4). Write your answer in component form.

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Q: Give the vector equation of the line passing through P and Q

A: To find the equation of the line passing through P and Q.

Q: Determine whether the lines L1 and L2 given by the vector equations are parallel, perpendicular, or…

A:

Q: The position vectors of the points A, B, C, D are given by a = 2i + 3j - k, b = 4j+ 5k, c = 7i-3k,…

A:

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: perpendicular to (x, y, z) = (1, -2,0) + r(1, -1, 1) through P(1, 3,5) [parametric equations]

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Q: 3. Find an equation of the plane passing through the points (1, 2, -6), (2, 3, -2), and (-1, 4, 8).…

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Q: What is the shortest distance d from the line L₁ defined by the vector equation to the line L₂…

A: Consider 2 lines in vector form as: v1 = a1 + c * b v2 = a2 + d * b here, c and d are the constants.…

Q: 3. Find the equation of the line that goes through the point (1, 3, 2) and is parallel to the line…

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

Q: Consider the line passing through the points (2, -3,4) and (5,10, -12). Describe the line by a.…

A:

Q: Find the direction of v:v =(7,-2)

A: Given: v→=7,-2

Q: х-2 у-4 Convert the symmetric equation of the line l: to the vector equation. 6. 7

A: Here we have to convert the symmetric equation of the line l:(x-2)/6=(y-4)/7 to the vector equation.

Q: 3) Find equations for the lines: a. The line through the point P(3,-4,-1) parallel to the vector…

A: Here we have to find the equations for the lines,  a) The line through the point P(3,-4,-1) and…

Q: Choose the equation(s) which have the following resultant vecto K 1 " Select one or more: C. * a.…

A: Given query is to find the resultant vector.

Q: Describe the graph of the equation. r = (6 – 21) i+ 10rj O It is a line in 2-space through the point…

A: Solution :-