9. (a) are perpendicular to each other. Determine the algebraic condition such that the vectors č= (-3, p, – 1) and d = (1, –4, q) (b)| If q = -3, what is the corresponding value of p?

Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

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Q: 'he sum and difference of two vectors à and B are equal in magnitude. Prove lgebraically that the…

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Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

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

A: Let's find.

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

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Q: 2. 1 show thet vectors cre linecrly dependent or lineerly in dependont

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Q: Let f(x, y) = 5y² In(4x). Then Duf(1,4) in the direction of the vector (-2,-2) is

A: The explanation of answer as follows

Q: Suppose that u and v are vectors in R7 both of length 2/2 and that the length of u- vis also2 /2.…

A: We can evaluate  the given problem as follows:

Q: 3. Two lines in the plane are perpendicular when the product of their slopes is -1. Apply this to…

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Q: 4. If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, and the angle at…

A: To calculate the angle we use dot product of two vectors given by Taking two vectors as U&V…

Q: Q1, Find Parame tric equations for the line through the Point (0,1, 2) that is U =i +2} + 3k and ū=…

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

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A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

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…

A:

Q: Suppose that u and v are vectors in R7 both of length 2√2 and that the length of u - v is also²√².…

A: Solution :

Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: The normal line to the surface x² + 2y² + ² = 25 at the point (1, -2, 4) is parallel to the vector O…

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Q: Find the vectorequationof the line of intersection of the planes  2x-3y–z=5 and x+y+2z=1

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Q: 6 2 Show that it is vectors are lineas dependent line or independent.

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Q: 1. The two unit vectors parallel to the line y = x- 3 are and

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: -x + 6y + 2z = 6 1. -x + 3y + z = 7 2 Find the normal vector, n,, to -x + 6y + 2z = 6. n = 1 Find…

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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: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

A:

Q: For which positive value of x are the vectors (-14x, 2, 1), (2, 3.x², –10) orthogonal?

A: Given:- vectors <-14x, 2,1> , <2, 3x2, 10> To find:- positive value of x when both…

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Q: 9. Which is traveling faster, a car whose velocity vector is 217 +35j or a car whose velocity vector…

A: We are authorised to solve only one question, please repost remaining questions Magnitude of vector

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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…

A: We have, L1: x=4-t, y=2t, z=2+t and L2: x=1+4t, y=3-8t, z=5-4t

Q: The plane with normal vector (4, 6, 7) containing the point (-5,-1,5) has equation Ax + By + Cz = D.…

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Q: Show that ū = aitbj is perpendicular to the line ax+by=C by establishing that the slope of the…

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Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

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Q: Show that the vector ñ = 2î – 3j is perpendicular (orthogonal) to the line 2x – 3y – 6 = 0.

A: to Show that the  given vector is perpendicular to the  given line

Q: 3. Compute the angle between vector a = (1,2,3) and the positive r-axis.

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Q: | Show that the vectors 2 do not span R³ by giving a vector not in their span.

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Q: Realize the Cauchy-Schwarz inequality for the vectors x= ( -1, 2, 4,3), y=(0,-2,1, 4) ∈ R4 and find…

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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

A:

Q: Is it always true that T(0) = 0 where the zero vectors live in the appropriate spaces? Justify

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Q: Find the equation of the plane in xyz-space through the point P = (5, 4, 3) and perpendicular to the…

A: NOTE: Refresh your page if you can't see any equations. . the normal vector is  . the given point…

Q: 2. Can three vectors in the xy plane R2, have u v < 0, v w < 0, w u<0?

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Q: find two distinct vectors on the line belonging to the intersection of the hyperplanes: Xi+ 2x2 - X3…

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

A: To show that the lines L1: x=4-t, y=2t, z=5+t and L2: x=1+2t, y=3-4t, z=5-2t are parallel and to…

Q: 20. Show that the pair of vectors ' and ¯J is perpendicular.

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Q: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: 9. Find both vectors of length 5 that are perpendicular to plane 2x + 2y +z - 4 = 0.

A: Explained below

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