Let I and g be unit vectors. Hence T-T= -G = 1. Calculate the inner products I (-1) and (T+g) - (T-7).

Q: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

Q: * Find the values for h for which the vectors are linearly dependent: 7

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Q: Let A and B be nonzero vectors. Find k e R such that A – kB is orthogonal to A + B.

A: We know if a vector P→ is orthogonal to another vector Q→ then scalar product (dot product) is zero.…

Q: Sketch the curve of the vector function r(t) = 3ti+ (3t + 1)j,-1<ts2, and indicate the orientation…

A: The given curve in vector form: r(t)=3ti+(3t+1)j The point of t is -1≤t≤2 To find the curve at the…

Q: find II u II for the given exercise, and give a unit vector in the direction of u.

A: According to the given information, first it is required to find ||u||.

Q: Find the real values of ,a,b,c that make the convolution equal to zero for the vector function F(x,…

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Q: Determine the constant a so that the vector i = (2x + 3y)î + (2y – 2z)j+ (x + 2az)k is a solenoidal.

A: Given : The vector v→ = (2x + 3y) i^ + (2y - 2z) j^ + (x + 2az) k^.   To determine the constant a so…

Q: State whether the following derivatives of vector-valued functionsr1(t) and r2(t) are scalars or…

A: To find:  whether the derivatives of vector-valued functions r1(t) and r2(t) are scalars or…

Q: Let L be the line y = 6 – 4x in R?. Find vectors a and b so that v = a+tb is a vector equation for…

A: Vector equation of line

Q: Find the velocity and acceleration vectors in terms of u, and ug- r= a(4+ sin t) and 0 =9- e -t,…

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Q: find II u II for the given exercise, and give a unit vector in the direction of u.

A: Now,

Q: Find the coordinate vector[x],of x relative to the given basis B= {bl,., bn}. --]--[}]--[1] bị = ,b2

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Q: Let c1 (t) = ei + 7 sin(t)j + t*k and c2 (t) = e-Sti + 5 cos(t)j – 7t*k. (Enter your solution as a…

A: Given: Let c1(t)=e5ti+7sintj+t4k and c2(t)=e-5ti+5cos(t)j-7t4k. To Find:      ddt[c1(t)+c2(t)]

Q: Let v = 2i - 5j and w = i - j.Decompose v into two vectors, v1 and v2, where v1 is parallel to w and…

A: v=2i-5j  and  w=i-j. Now, v·w=2i-5j·i-j=21+-5-1=2+5=7 &amp; w=12+-12=2

Q: Q1:- Find the domain of the following vector functions:- (a) f(t) = (cos nt)i – Ln(t)j + vt – 2k %3D

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Q: Consider the vector v = 1 and the vector "function" w(k) = 1 For what value of k are i and w(k)…

A: Two vectors v→ and w→ are said to be orthogonal if v→·w→=0 Given v→=111w→=11k

Q: Find all value(s) of t such that the vectors 2t i – 2 j– k and 2ti+ 3t j – 2k are nernendicular

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Q: Decompose V into in two vectors V1 and V2, where V1 is parallel to W and V2 is orthogonal W. V=2i+j…

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Q: Find the domain of the vector functions, r(t), listed below. using interval notation. a) 1 r(t) = (…

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Q: Let i = 47 – 11 and y = 4j – 10k be two vectors. Find the value of the scalar product x · y.

A: See the detailed solution below.

Q: products

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Q: Prove that the vector T′(t) is 0 for an object moving in a straight line.

A: Here an object moving in a straight line. The path of the object can be given as follows.…

Q: Find the real values of a,b,c that make the convolutio equal to zero for the vector function F(x, y,…

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

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Q: Find the spacing and involution for the following vector functions 1- ƒ(x, y, z) = (xi + yj + zk]…

A: Topic:- vector

Q: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

Q: Find a non-zero vector x perpendicular to the vectors  v= [-3]    And u = [-1]      [11]…

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Q: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

Q: 1 (b) Find the span of vectors i = |0 and j = |1 in R3

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Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

A:

Q: Let v = 2i - 5j and w = i - j. Decompose v into two vectors, v1 and v2, where v1 is parallel to w…

A: Given vectors are: v = 2i - 5j and w = i - j The formula for the vector projection is given by…

Q: H.W 3- Find a vector V =xi +yj +k that is orthogonal to both A = 3i + j +k _and B = 3i +2j +2k .

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Q: Given the vector-valued functions - 4t ü(t) = e-i+ e-j – tk ö(t) = tỉ – 4tºj + 3k -21 %3D (i(t) ·…

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Q: Give the two unit vectors u such that the function z = g(x, y) of example 3 has zero derivatives at…

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Q: If r(t) = (1 + t)/²i+ (1- t)/2j+tk, t 0 then the binormal vector B is اخترأحد الخيارات

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Q: Find a vector function that satisfies the conditions r"(t) = 12ti – 31-/2j+2k, r'(1) = j, r(1) = 2i…

A: We have to find a vector function that satisfies the conditions…

Q: In Fn, let ej denote the vector whose jth coordinate is 1 and whose other coordinates are 0. Prove…

A: If we can show that  {e1, e2, . . . , en} is linearly independent in Fn then we can say that  {e1,…

Q: Consider the vectors cO 1 (2 1 2) (1 1 0) in R3. Find the value of c, for which given vectors are…

A: The given vectors,c01, 212, 110

Q: Show that the vectors v1, V2, and v3 are linearly dependent, where n- . -. 3 V2 = 5 and v3 = 6 Vi =…

A: The given vectors are v1=12, v2=34 and v3=56

Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: For the vector valued function given by 7(t) = (,-1, In t) and u(t) = (t²,-2t, 1) find %3D %3D…

A: Given that r→t=1t, -1, ln t and u→t=t2, -2t, 1 We can write the given vector as r→t=1ti +-1j+ ln tk…

Q: Find the cosine of the angle between the vectors P1(x) = 1 + 2x – x² and p2(x) = -1 – 3x + 2r² with…

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Q: А. Find the domain of the vector position r(t) + t+2 (t + 2) j + In(9 – t²) k

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Q: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

Q: Find a vector n normal to the plane with the equation x+6y + 4z = -10. n= 00> (1₂)

A: Concept: The equation of the plane is written as: ax-x0+b(y-y0)+c(z-z0)=0 or ax+by+cz=d Here the…

Q: Find the vector, not with determinants, but by using properties of cross products. (i × j) × k

A: The given expression is i×j×k To find the vector product of the expression, first we simplify the…

Q: Find the vectors T and N and the binormal vector B = T × N for the vector-valued function r(t) = ti…

A: first, we will differentiate the vector r(t) we get  r'(t)=i+2tj+t2k doing the modulus we get…

Q: find II u II for the given exercise, and give a unit vector in the direction of u.

A: