19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

Q: according to what you learned from the vector addition experiment, if we have vectors à = 2.4x – 3ŷ…

A: Given that,a→=2.4x⏞-3y⏞b→=4x⏞+5.5y⏞x⏞ and y⏞ are unit vectors representing positive x and y…

Q: What is the unit vector perpendicular aial yA n = i-j+ 3k, n2 = 2i + j + 3k to the vectors?

A: Given that:n1=i-j+3k,  n2=2i+j+3k

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: Determine if i = (1,0.-4) and w=(9,3,1) are parallel vectors.

A: Use the vector product to show the given vectors are parallel.

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…

Q: In general, show that the vectors V = ai + bj and W = -bi +aj are always perpen-dicular. Assume a…

A: Given vectors are v=ai+bj and w=-bi+aj, where a≠0 ,b≠0. We know that two vectors are perpendicular…

Q: 13. Show that the pair of vectors i + i and i – i is perpendicular.

A: Two vectors is said to be perpendicular if their scalar product is zero.

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: 4

A: We are given the following vectors.

Q: The cross product of the vectors a = 2i - j+ 3k and b= 4i – 2j + 6k is likely to be the zero vector…

A: If vectors are parallel then cross product will be zero check they parallel or not

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: 1. Show that the necessary and sufficient condition for two nonzero vectors A and B to be…

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: and = Wnte Pas the sum of two orthogonal vectors, 2 in S panƐu} and orthogonal to .

A: Given that y→=51 and u→=36.It is required to write y→ as the sum of two orthogonal vectors, x1→ in…

Q: Prove that two vectors v = (a, b) and w = (c, d)are perpendicularif and only if ac + bd = 0

A: We prove the above statement using the concept of dot product or scalar product of two vectors. The…

Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

Q: The vectors į+j and i-į are perpendicular. True False

A:

Q: Sketch the vector b = <3, 4> based at P = (−2, −1).

A: Sketch the vector b=<3, 4> based at P=(−2, −1).

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: 24. Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in Figure 16, and…

A: The vectors v and w are in the x-z plane. The cross product of both vectors will yield a vector…

Q: Consider the vectors x1 = (8, 6)T and x2 = (4, −1)T in R2. Let x3 = x1 + x2. Determine the length of…

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:

Q: 42. Show that the unit vector ī = xỉ + yj is not parallel to ū = yi – xj for any choice of x and y.

A:

Q: Find the smallest positive angle between the given pair of vectors. (3,1) , (4,6)

A: The given pair of vectors are,

Q: c) Show that vector ū = 1 cannot be expressed as a linear combination of 2 in R3 3 vectors vi 1 and…

A: we have to show that , we can not write as a linear combination of vectors v1 and v2

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: 4. If two vectors P = 4i + 6j - 8k and F = 6i - 8j • 4k are added together describe the…

A: As we are solving only one problem at a time please submit the other question one by one as you…

Q: The cross product of two vectors 3i + 4j -5k and -i+j- 2k is * 3i -11j +7k O 31 +11j +7k O 31 -11j…

A: Use Cross product of vector

Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

A:

Q: What can be said about non-zero vectors ū, v and w if (ūxv)· w = 0?

A: Here use the definition of cross product and dot product of vector

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

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: 1) in triple dot of vectors |(A x B).C| = |(C x A). B|, where the vectors %3D A,B, and C are not…

A:

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

A:

Q: 10. Which of the vectors U =, V = and W = are in the same plane?

A:

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

A:

Q: 9. Show that for any real numbers a and b the vectors u = ai and v = bj are orthogonal?

A: Topic:-  vector algebra

Q: Q1) If the vectors A, B, C and D in the same plane, prove (AxB) x (CxD) =0?

A:

Q: O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

A: Our are objectives to check which vectors are parallel and which vectors are perpendicular

Q: 41. Find the value of A if the vectors i+ Aj+3k and-2i+j-4k arc parallel. uectors ii + 3k and 2i -

A:

Q: Compute the distance between the following vectors: 2 2 w = 3 v = -4 1

A: Hope it is useful

Q: 9. Find two unit vectors that are perpendicular to both j + 2k and i – 2j + 3k.

A: A vector perpendicular to both of the given vectors can be found out by finding the cross product of…

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: A n = i-j+3k, n2 = 2i +j+ 3k to the two vectors.

A:

Q: 17 jp 17 Jlgull>> حفظ الإجابت 3 درجات Two vectors ñ and m are said to be parallel if ñ m-0

A:

Q: Let a = and b = -2 be two vectors. What is Ja2|b|2 - Ja b2 ?

A:

Q: 64. Show that if u + v and u – v are orthogonal, then the vectors u and v must have the same length.…

A: here, the given vectors, A =u+vB=u-v given that, they are orthogonal, that is, A·B=0u+v·u-v=0⋯⋯1

Q: Let b = 4i + 3j and c be two vectors perpendicular to each other in the xy-plane. All vectors in the…

A:

Q: O Are the three vectors: V= 4i-8j+kV= 2i+j-2k and ū;=3i-4j+12K in the Same Plane?

A:

Q: Show that for any two vectors u and v: = |

A:

Q: Find a so that the vectors v = i- aj and w = 7i + 7j are orthogonal. ..... une on integer or o…

A: If two vector orthogonal then dot products will be zero

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.