Let v = (5, 8) and w = (4, 5). What is the dot product v · w?

Q: Let x→=8i→−11j→ and y→=4j→−9k→  be two vectors. Find the value of the scalar product x→⋅y→.

A: We have to find the scalar product

Q: Evaluate where x; are Cartesian components of a, and x = |æ|.

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Use the properties of the dot product to evaluate the expression, assuming that u · v = 2, ||u|| =…

A: Given that, u · v = 2, ||u|| = 1, and ||v|| = 3. To find, u · (4v)

Q: By using the properties of dot and cross product, prove the following: c) W⃗ ×(V⃗ ×U⃗ )=(W⃗ .U⃗ )V⃗…

A: To prove :  W×(V×U)=W .U)V −(W .V)U

Q: Use the dot product to determine whether v = i + j and w = -i + j are orthogonal.

A:

Q: Let T: R2 R2 be a reflection in the line y = x. Find the image of each vector. (a) (3, 1)

A: (a)  (1, 3) (b)  (-1, 0) (c)  (0, -a) (d)  (b, 0) (e)  (-d, c) (f)  (g, -f)

Q: Use the dot product to determine whether v = 5i and w = -6j are orthogonal.

A: Given:

Q: Use the properties of the dot product to evaluate the expression, assuming that u · v = 2, ||u|| =…

A: dot product: a→.b→ = abcosθ θ is angle between a→ and b.→ u · v = 2 ||u|| = 1  ||v|| = 3

Q: Let U(7, 6, -5), V(2, 8, -2), and W(1, 10, o). calculate the scalar triple product U.(VxW) Answer:

A: Given that  The vectors U(7,6,-5) V(2,8,-2) and W(1,10,0) To find the U(V*W)

Q: Find the cross product u x 7 where u = 51 -3j+k and = (-1, -3,2). uxv=

A: To find the cross product u→×v→ where u→=5i-3j+k and v→=-1, -3, 2.

Q: The scalar product 0v is 0.

A:

Q: Compute the dot product u v. 11) u- o v A) 30 B) 23 9 18 D) 0

A: 11) Here the equations ; u = <u1, u2, u3> = <12, 0, 6> v = <v1, v2, v3> = <2,…

Q: Find the area of the parallelogram spanned by vectors v and w suchthat ||v||=||w|| = 2 and v · w =…

A:

Q: Use the dot product to determine whether v = 2i - 2j and w = -i + j are orthogonal.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Let v = -7i - 7j-3 k and w =-3i+ 4j +6 k. Then the vector v – w can be written as

A: note : vector addition or subraction can be performed as  a⇀+b→ = (ax+bx,ay+by,az+bz) similarly for…

Q: Find the cross product a x b. a = (4, 5, 0), b = (1, 0, 7) Verify that it is orthogonal to both a…

A: We can make it easier for you

Q: use the properties of the dot product to evaluate the expression, assuming that u · v = 2, u = 1,…

A:

Q: Explain why each expression involving dot product(s) is meaningless. Assume that u and v are vectors…

A:

Q: products

A:

Q: Find the dot product of u and v. u=4i-3j v=i-j

A:

Q: please help me with this exercise

A: Given,

Q: Find a vector B such that F = V × B and V · B = 0, where F %3D (x + Зу, у — 2z, х - 2z).

A:

Q: Find the dot product 9) v = 12i + 9j, w = -10i – 8j

A:

Q: Find the dot product v*w and the angle between v and w. v = i + j, w =i + j - k

A: Given: v=i+jw=i+j-k To Find: The dot product of vector v and w and the angle between v and w.

Q: If u- i+ j+ k, v= 10 i +4j+6 k, y w= 8 i+9j+7 k, evaluate the dot triple product (u x v) - W. 86…

A:

Q: Use the dot product to determine whether v = 3i and w = -4i are orthogonal.

A: Let "." represent the dot product Dot product = v.w Two vectors u and v whose dot product is u·v=0…

Q: Use the vectors a = [-1,0,1], b = [1,-1,5], and č= [0,-1,-2] to prove that a(bxč) # (åxb)xč

A: The answer is given below:

Q: If w = -2i + 6j, find the vector: [2(-2) + 4(-6)]w/lwl2.

A:

Q: Find the component form of the vector v given ||v|| = 12 following the direction of u (3, –5)

A: Find the component form of the vector v given ||v|| =12 following the direction of u = (3,-5)

Q: Find the dot product v • w. v = 7i - 3j, w = 8i + j %3D O -17 O 53 O 59

A: Here I am attaching image so that you understand each and every step.

Q: Find the component form of the given vector. v = y 4 3 1 2 4 3.

A:

Q: Find the dot product v • w. v = 6i + 8j, w = – 13i – 8j O A. - 78 А. О В. - 14 О С. -64 O D. - 142

A: Explanation of the answer is as follows

Q: Find the dot product v • w. v= i+ 3j, w= 7i -j

A: Given,           v=i+3j , w=7i-j

Q: Find the cross product a × b. a-i-j-k, b-tj+* Verify that it is orthogonal to both a and b. (a x b)…

A:

Q: Find the dot product, U⋅V U=, V=

A: The dot product is a scalar operation. The dot product gives the unique value (number) as the…

Q: If a, and b are non - collinear vector and vectors a = (x +4 y)a +(2x + y +1)b and, B= (-2x + y + 2…

A: We will solve the following

Q: Use the dot product to determine whether v = 8i - 4j and w = -6i - 12j are orthogonal.

A: Two vectors are orthogonal when its dot product is zero.

Q: ..) Find a vector ğ so that if F{f} = (co, C, C2, C3) then Ff ® ğ = (co, 0, 3c2, 0). %3D 160

A: The objective is to find the vector g so that is F(f)=(c0,c1,c2,c3) Then, Ff⊙g=(c0,0,3c2,0) It is…

Q: Calculate the cross product. (i - 9j + 6k) x (j – k)

A:

Q: Find the component of u along v. u = 31 - 24j, v =j

A: component of vecor u along vector v is=u→.v→v→givenu=3i-24jv=j

Q: Find the vector projection, Proj;A and ProjĄB When A = i+ 2j + k and B = k. 1.6

A:

Q: Use the dot product to determine whether v = 5i - 5j and w = i - j are orthogonal.

A: Orthogonal vectors: Two vectors are orthogonal if there dot product is zero.

Q: Find the dot product v • w. v = i+ 4j, w= 7i -j O A. 11 В. О С. 3 O D. -3

A:

Q: Show steps clearly.

A: To find the dot product of the given vectors.

Q: Find the dot product v•w and the angle between v and w. v= -i+4j- 2k, w = 3i +j+4k

A:

Q: Which vector is not collinear with [c, d]? O [2c, 2d] O(-c, -d] O [10c, 10d] O [d, c]

A:

Q: Find the cross product a x b. a = j + 6k, b = 31 - j + 2k Verify that it is orthogonal to both a and…

A:

Q: Use the dot product to determine whether v and w are orthogonal. v = - 2i + 2j, w =i-j

A: Given,          v=-2i+2j , w=i-j

Q: Find a nonzero column vector u such that Cu = 4u.

A:

Q: Use the dot product to determine whether v = 3i and w = -4j are orthogonal.

A: To check: whether the two vectors  v=3i and w=-4j are orthogonal or not. Concept used: The two…