a)) Find the length and direction (when defined) of (uxv) and (vxu) 1. u = 21 – 2j - k, v =i-k 2. u = 21 + 3j. v = -i + j 3. u = 21 – 2j + 4k. v = -i +j- 2k

Q: In Exercises 1–2, find the length and direction (when defined) of u * v and v * u. 1. u =-8i - 2j -…

A: find the length and direction (when defined) of u * v and v * u.

Q: ow that c=3i -2j1+k and d=2j+ 4k are orthogonal.

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Find the length and direction (when defined) of u x v. u = 2 i+ 2j- k, v = -i+ k

A: As per our guidelines we are supposed to answer only one question and rest of the questions are…

Q: Find the length and direction (when defined) of u x v and vxu. u= 5i + 3j – 5k, v=0

A: we know that  uxv=|u|.|v|sin∅.n^where ∅ is angle between u and v and n^ is unit vector perpendicular…

Q: Find the length and direction (when defined) of u xv and v×u. u= - 8i – 4j – 3k, v = 3i + 3j + 4k

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Q: 11. Use vectors to show that the distance from P:(x1, yı) to the line ax + by = c is |ax, + by, – c|…

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Q: Let a = ci + j and b = 2i + 10j. Find c so that a and b are orthogonal. c =

A:

Q: Find the length and direction (when defined) of u x v and vxu. u= - 12i + 9j – 12k, v = - 4i + 3j –…

A: Using formula of u x v and v x u,

Q: In Exercises 1–8, find the length and direction (when defined) of u X v and v X u. 1. u = 2i – 2j –…

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Q: Let a = ci + jand b = 7i + 49j. Find c so that a and b are orthogonal. C = i

A:

Q: Let a = ci + jand b = 9i + 36j. Find c so that a and b are orthogonal. %3D

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Q: 4. Given that lines PQ and RS are parallel and t is a transversal, use a two column proof to prove…

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Q: Find the divectional desivative of div (anadF) he point (1,1,2) in the direction of 3 2 at The -i+…

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Q: Let a = ci + jand b = 7i + 35j. Find c so that a and b are orthogonal. C = i

A: Dot product of two vectors

Q: Let a = ci + jand b = 2i + 14j. Find c so that a and b are orthogonal. i

A: Given that,a=ci+j and b=2i+14j

Q: For any vectors u, v and w, show that uxv=uxw does not always imply v = w. Prove that u v ≤ ulv, and…

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Q: Let a = ci + j and b = 3i + 3j. Find c so that a and b are orthogonal. %3D C = i

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Q: Show that the vectors u=, v= , and w= satisfy the following properties of the cross product. и хи30…

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Q: Let a = ci +j and b = 7i + 28j. Find c so that a and b are orthogonal. c =

A:

Q: Given v = (8, –3) and w = (12, -4), find vector projection of v onto w.

A: Solution; Consider the given vectors :  v = 8, -3 and w = 12, -4 Now, vector projection of v onto w…

Q: a) Prove that ||u + v|| = ||u - v|| if and only if u and v are orthogonal, (b) Draw a diagram…

A: a) Suppose u,v are orthogonal. Now…

Q: 2) Determine the value of a so that A = 2i + aj + k and B = 4i – 2j - 2k are perpendicular.

A: This question is based on dot product application.

Q: Find u × v and show that it is orthogonal to both u and v.u = (4, 1, 0), v = (3, 2, −2)

A: Now cross product is,

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

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Q: Show that the vector v = ai + bj is parallel to the line bx - ay = c

A: Find the slope of the given vector v=ai+ bj is given by ba.

Q: Given: rl s, tls Prove: r || : 1 4 7. 6

A: It is required to prove that r parallel to t.

Q: Let ABCD be a trapezoid with parallel sides AB and DC. Suppose that the length of AB is 20…

A: Two lines which never intersects each other are considered parallel lines. And the distance between…

Q: Find the length and direction (when defined) of u xv and vxu. u= - 12i + 8j – 20k, v = - 3i + 2j -…

A: To find the length and direction of u→×v→, first find the value of u→×v→ by cross product. The given…

Q: Let a = ci + jand b = 6i + 54j. Find c so that a and b are orthogonal. C = i

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Q: Suppose that two lines Re((1+i)z+2i+3) = 0 and Re(2-bi)z+5) = 0 are perpendicular. then b=.

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Q: Let u = i - 2j, v = 2i + 3j, and w = i + j. Write u = u1 + u2, where u1 is parallel to v and u2 is…

A: u1 is parallel to v and u2 is parallel to w.So u1= av and u2=bwWhere a and b are constants.

Q: Let a=ci+ja=ci+j and b=9i+45jb=9i+45j. Find c so that a and b are orthogonal.

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Q: For any vectors u, v in R', we havelu + ū|? = [u|2 + [ū]2 True False

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Q: Let a = ci + jand b = 9i + 54j. Find c so that a and b are orthogonal. c = i

A:

Q: If u • vx w or v • or w • v equal to zero, then the vectors u, v , and w are coplanar... True False

A: Concept Used: Three vectors are said to coplanar if their scalar triple product is zero That is  [u→…

Q: What is the Cartesian Product of Z × X × Y, where X = {3,–1}, Y = {m, l, 0} and Z {w,b}.

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Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k,…

A: (a) To show that triangle ABC is a right angled triangle, use scalar product of vector, that is…

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: Let a = ci + jand b = 6i + 30j. Find c so that a and b are orthogonal. c = i

A: The vectors are given by a = ci+j b = 6i+30j Condition for orthogonal vectors:  a·b = 0 To evaluate:…

Q: Find the cross product ax b. a - (1, 1, -1), b= (6, 8, 10) Verify that it is orthogonal to both a…

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Q: Find the length and direction (when defined) of u x v. u = -,i + +k U = i + j + 2k ||uxo ||= 8 | ||u…

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Q: For the vector PP, , its norm satisfies PP, =2. The inscribed angles between PP, 2 2 and x-axis and…

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Q: 4.15. Given vectors u = and v =, find the projection of u onto v.

A: Proceed as shown below...

Q: given vectors u=4i-j and v= 3i+3j compute the projection of v onto u?

A: Given, vector u and v

Q: Find u × v and show that it is orthogonal to both u and v.u = (12, −3, 1), v = (−2, 5, 1)

A: Given vectors u=12,-3,1v=-2,5,1 Their cross product is u×v=ijk12-31-251…

Q: In Exercises 1–5, find the length and direction (when defined) of u * v and v * u. 1. u = 2i - 2j -…

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

Q: Given vector u (4, –1) and v = (-1, –5) , determine the value of v + 2u in component form.

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Q: For what values of aare u and v orthogonal?

A: Consider the given vectors  u=11-2  and  v=a-12 Write the vectors in row form u=1,1,-2  and…

Q: For what values of y are the vectors yi – 2j + 3y k and 6i +j+ 3y k orthogonal.

A: To find the values of y for which the vectors yi-2j+3y k and 6i+j+3y k are orthogonal.