Find the value of  x  so that the two vectors  (27,1,13)  and   (x,0,1)  are orthogonal

Q: Find a non-zero vector a perpendicular to the vectors [3] and ū = 2 1

A: Given, v→ = 372  and  u→ = 121   We have to find the non zero x→ vector perpendicular to both the…

Q: Find the two unit vectors orthogonal to both a = (3, 1, 1) andb = (−1, 2, 1).

A: Given: a=3,1,1 and b=-1,2,1

Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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Q: Find two vectors v1 and v2 whose sum is ⟨−3,5⟩, where v1 is parallel to ⟨1,−1⟩ while v2 is…

A: Given Data: The sum of vector v1 and v2 is <-3,5>. The vector v1 is parallel to the vector…

Q: Find two linearly independent vectors perpendicular to the vector 1 3

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Q: 1 Y

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Q: Determine ä xb and bxå. Confirm that the cross product is orthogonal to each vector. ā=[4, –3, 5],…

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Q: Find two vectors v1 and v2 whose sum is ⟨−5,0⟩, where v1 is parallel to ⟨5,1⟩ while v2 is…

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Q: Find a nonzero vector parallel to the line of intersection of the two planes 3x−3y−4z=5 and…

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Q: Find the cross products u x v and v xu for the vectors u = (4,4,0) and v = (0,2, - 5).

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Q: Find two vectors v1 and v2 whose sum is (2, –5), where vj is parallel to (5, 2) while v2 is…

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Q: The cross product of two vectors in R yields a scalar. True False

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Q: Find the x-component of the vector of length 3 in the direction of V = (-1,-1).

A: v=<-1,-1>=-i-j Unit vector in the direction of vector V i.e.,     v⏜=-i-j(-1)2+(-1)2 =-i-j2…

Q: Show that the vectors 1 – t,1+ 2t² , t² +t+1, t² + 2tare linearly dependent and indicate how one of…

A: Given Vectors:V1 = 1-tV2 = 1+2t2V3 = t2+t+1V4 = t2+2tgiven vectors are linearly dependent, then…

Q: Find a non-zero vector x perpendicular to the vectors 3 13 and u =| 4 -4 3

A: Let's find.

Q: Find two unit vectors orthogonal to both v (1,1,-1) and w-(2,-1,1).

A: Calculation:Compute the two unit vectors as follows.

Q: Find the value of t such that the vectors v=(2t+1,-3,3t-2) and w=(7,4t+2,2) are orthogonal.

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Q: Find the equation of the plane sanned by the above two vectors

A: Given: Two vectors u=223 and v=-20-3. To find: Equation of plane spanned by given vectors.

Q: Find a vector v parallel to the intersection of the planes - (x + 3y + 4z) = 7 and 2y – 2x + 2z = 7.…

A: The direction vector of the line of intersection of two planes is parallel to the cross product of…

Q: Find two linearly independent vectors perpendicular to the vector V = 3 -5

A: Let's find.

Q: Find two linearly independent vectors perpendicular to the vector 4 v =

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Q: Find a vector in the plane parallel to the line ax + by = c.

A: We know that, Slope of parallel lines are equal Given equation of line is ax + by = c Slope of this…

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: 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…

Q: Find the orthogonal projection of the vector (2,4) about the line L parallel to the vector (-1,2)

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Q: Find the value of c that will make the vector 2 lie in the span of 0 2 and

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Q: Determine all vectors v that are orthogonal to u.u = (11, 2)

A: Now let

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: . Suppose ū = and i = ;). Construct a pair of orthogonal vectors from these two vectors.

A: See below the answer

Q: Find all orthogonal vectors to u=(2, -3).

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Q: Find two linearly independent vectors perpendicular to the vector 4 -7

A: This question can be solved using the concept of linearly independent vectors.

Q: Find a vector that is orthogonal to both v = (1, –2,3) and w = (2, 1, –1).

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Q: Find two independent vectors both of which are perpendicular to i = 3

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Q: Find two vectors j and 02 whose sum is (-3, -4), where j is parallel to (0, 5) while 02 is…

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Q: Find the value of h for which the vectors are linearly dependent

A: The given vectors are 1-14 , 3-57 , -15h The vector v3 are linearly dependent if the equation…

Q: Find non-zero vectors I and 7 that are both orthogonal to and orthogonal to each other.

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Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

A: If we have a set of vectors v1, v2, v3, ..., vn, then they are said to be linearly dependent if…

Q: Find a vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2)

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Q: Find a unit vector that is orthogonal to both u = (2, -8, 6) and v = (4, 10, -6).

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Q: Determine the vectors axe linear yy independent -3 2. 8. O ON

A: For linearly dependent determinant  of matrix is zero D=0

Q: Write the vector v= 1 as the linear combination of vectors --0 w =

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Q: u

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Q: Determine whether the vector v = 8 is spanned by the vectors and 3 or not.

A: Given three vectors and we have to find if  v=789 is spanned by111 and 123

Q: Find two vectors ūj and īz whose sum is (-5, –3), where vj is parallel to (2, 5) while īz is…

A: To find - Find two vectors v1¯ and v2¯ whose sum is -5, -3, where v1¯ is parallel to 2, 5 while v2¯…

Q: Show that if x and y are two vectors, then

A: To show : If x and y are two vectors, then x-y≤x±y≤x+y Pre-requisite :  Cauchy-Schwarz inequality…

Q: Write y as the sum of two orthogonal vectors, x1 in Span{u} and x2 orthogonal to u

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Q: Solve for the linear equation of the plane through the origin and perpendicular to the vector…

A: Topic:- geometry