For which positive value of r are the vectors (14r, 2, -1), (2, –3r², –10) orthogonal?

Q: Consider the vectors v, = (1 0) and v, = (0 1) in R,. the vector ( 0.4 3.7) can be written as a…

A: Linear combination

Q: a) Find equation of the Line through point (2,3,0) perpendicular to the vectors U1 = i+2j+ 3k and U…

A: Line through point (2, 3,0)  Which perpendicular to U1 and U2

Q: 4. Find the value of t such that the vectors ~v = h2t + 1,-3,3t - 2i and w = h7,4t +2,2i 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 equation of the plane that contains the point (4, – 1, 3) and is perpendicular to the…

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Q: find the value of k for which the vectors u and v are orthogonal.  u = 2i - kj v = 3i + 2j

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Q: Find the component form of the vector.The vector PQ , where P = (1, 3) and Q = (2, -1)

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Q: 2. For the vectors u = -5i + k and v = 3j - 4k, find a. (u · v)u b. u - 3v

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Q: For what values of h the vectors -3.72%3D linearly independent are

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Q: find the acute angle between the given linesby using vectors parallel to the lines. 2 - x + 2y = 0,…

A: 2-x+2y = 0⇒2y = x-2⇒y = x-22⇒y = x2-1             --(1)So, vector parallel to (1) is a→ = 12i ,…

Q: Find the B-coordinate vectors of ei and e2, where and B : %3D %3D %3|

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Q: [:] [] Find c so that the vectors and are parallel.

A: Find c so that the vectors c4 and 25  are parallel. Let u=c4 and v= 25 be two vectors. Two vectors…

Q: 4. Given that '(t) = (6t², 2t + 4) and that (2) = (2, 8), find r(t), where we are assuming that the…

A: We have to find the r(t)

Q: Suppose vectors v, w, and z sum to the zero vector. If v = 8.2i - 3.8j and w = 4.1i + 1.3j, find z.

A: We have to solve

Q: Find the angle 0 between vectors u = 2i - jand v = 6i + 4j.

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Q: For what values of c are the vectors [-8, c, 4] and [c, c²,c] orthogonal?

A: For orthogonal,dot product of vectors is equal to zero.

Q: Find the angle between the vectors u = /2i - 9j and v =v2i+j-2k.

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Q: Find the values of x such that the angle between the vectors u = (2, 1, -1) and v = (1, x, 0) is…

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Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: Q1: If , r₂ and r₂ are three parallel vectors of the same magnitude Prove that ₁+₂+3 is equally…

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Q: Find the equation for the plane through the point Po = (2,2,7) and normal to the vector n= 8i + 3j +…

A: Equation of plane passing through point P(x0,y0,z0) and normal to vector n=ai+bj+ck is given by:…

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

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Q: Show all work to calculate the value of x that makes the two vectors orthogonal to each other. v =…

A: Orthogonal vectors: Two vectors a→ &  b→ are said to be orthogonal if they are perpendicular to…

Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

Q: latél Show that if a is perpendicular to each of the vectors and then a is perpendicular to 26 +4

A: The detail solution is given below

Q: Find the median AD of the triangle ABC where positive vectors of the vertices A, B and C are…

A: Vertices of the Triangle ABC given A=i+j,B=4i+6j,C=i-j; Hence, We can take these vectors as the…

Q: Find the angle between the two given vectors. u = (1, –4, 1), v = (0, 2, –2)

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Q: Find the angle between the two vectors u 2i+ j-7k and v =i-j+ 4k

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Q: Q2. (d) Show that u=(-2,3,1,4) v=(1,2,0,-1) and are orthogonal vectors in R4.

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Q: The unit vector which is perpendicular to both r1=8ax+3ay-2az, * r2=2ax+7ay-6az is equal to a)…

A: Given That: The unit vector is perpendicular to r1=8ax+3ay-2az & r2=2ax+7ay-6az

Q: 1. Assume the lengths of the vectors 2a – b anda+ 3b , assuming a = (2,1,3) and b = (-1,2,2)

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

Q: 1 -E---Fl 2 V2 = 0 , and v3 = -5 span R³? Why or why not? 3 Do the vectors V₁ = -31

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Q: -) THREE VECTORS A, B, AND C ARE RELATED AS FOLLOWS ! A AT 180°, A +C =-5+j15, 2 C = CONJU GATE OF…

A: Solution :-

Q: 27-j+4k sī +2j-2k.

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Q: For the vectors u = (- 1,3) and v= (-4,2), calculate proj,u and scal,u. proj, u = D

A: Vector and scalar projection

Q: Determine the angle between the vectors: x 3i + -3j + -7k and y = 12i + 3j +11k

A: x = 3i -3j -7k  y = 12i +3j +11k

Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

Q: Find the angle between the vectors i + j + 2k and 2i - j +k

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Q: 3. Find the angles between the vectors: u = 2i + j, v = i + 2j – k а. -

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Q: Q1// Determine äxb if å=3i-5 j+7k and b=2i-6j+4k and check if resultant vector are perpendicular to…

A: Given,           a→=3i-5j+7k and b→=2i-6j+4kTo find: a→ × b→

Q: Find the values of ( x ) such that the vectors and are orthogonal.

A: Given: The two vectors are: 3,2,x and 2x,4,x Also, the two vectors are orthogonal.

Q: Find the dot product of the vectors v = 5i - 3j and w = 2i - j.

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Q: For the vectors ü = 2î + 3j – 2k ö = -Sî - 2j – 7k w = 3î + j – 9k the value of [(- ü) x (u – w)].…

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Q: Find a vector B for which that is parallel to A =-6i +3j –2k but has the opposite direction.

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Q: For the non-zero vectors A and B to be perpendicular to each other, the necessary and sufficient…

A: Given, For the non-zero vectors A and B to be perpendicular to each other, the necessary and…

Q: Use the points P(3, 1) and Q(7, 1) to find position vectors equal to PQ and QP.

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Q: Find the angle 0 between the vectors a = 8i – j– 4k and b = 2i+j- 9k. %3D

A: A vector is a mathematical concept with both magnitude and direction. It's used to describe things…

Q: Find the angle a between the vectors 3 a || -1 -2 - and 1

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Q: find the component form of the vector. The vector PQ, where P = (1, 3) and Q = (2, -1)

A: The component form of a vector XY with X=x1,y1 and Y=x2,y2 is defined as follows: <x2-x1,…

Q: R) Find the area of a triangle formmed from the two - = c'+2j=k-- - 2i-jtuk. Vectors-a- 6 = 2i-j+4k,

A: Given: a=i^+2j^−k^b=2i^−j^+4k^