Find the unit vector u in the direction of v. Verify that u| =1. 12. (1,–6)

Q: 2) A function is given by f(x, y) = xy - x-4y+4. If Duf(0,0) = 1, find the unit vector directions…

A: According to question,Given function,fx, y = xy - x -4y +4,Du f0, 0 = 1

Q: Find a vector-valued function whose graph is the indicated surface.

A: In polar coordinates, Using this rule, using appropriate substitutions:

Q: Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval…

A: Given vector function isrt=ln19t,t+8,17-tfind the domain.

Q: Find the domain of the vector function 7(t) = (v4 – t², e-3t, ln(t + 1)

A:

Q: Q1/ If f(x,y)=find a unit vector u for which Duf (2,3) = 0 x+y

A: We have to find a unit vector u for which Duf(2,3)=0 where f(x,y)=yx+y

Q: The Ū = ( 3 is a unit vector in the 3 Jī3 direction of (2, 3). Select one: True False

A:

Q: Find a vector-valued function whose graph is the indicated surface. The cylinder 9x² + y² = r(u, v)…

A:

Q: Find the value of x so that the vector i+2j+xk   makes and angle  pi/4  of  with the positive…

A: i+2j+xkTo Find: Value of x so that the vector makes an angle of π4 with the positive z axis.

Q: Find a vector equation for the line segment from (2, -4, 6) to (5, 5, 5). (Use the parameter t.)…

A: a→=2i-4j+6kb→=5i+5j+5kn→=b→-a→=3i+9j-k

Q: Find the unit Vector e(subv) where v=(2,2,1)ev=?I appreciate the help in advance

A: Formula used:Unit vector in direction v is

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B. N

A:

Q: Q2) Find T N „B of the vectors the curve r(t) = at the point (1, ,1)

A:

Q: 28. Find the unit vector in the opposite direction to 7 –j + k.

A: We will solve the following

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 a unit vector in the direction in which f (x, y) = 4 – 4:x² – 4y? decreases most rapidly at…

A: The direction in which the function  f(x,y)=4-4x2-4y2 is -∇f(x,y).

Q: Q2) Find the T „N of the vectors curve r(t) = at the point (1, 1)

A:

Q: Find the vectors T and N and the binormal vector B = T × N for the vector-valued function r(t) = 2…

A:

Q: Q2) Find the vectors the curve r(t) = at the point (11) of

A: First of all find r'(t) and the length of r'(t). Here, r'(t)=<2t,2t2,1> |r'(t)|=4t2+4t4+1…

Q: 5) Consider the vector function r = (9 — 2t, 4 + 2t, √√2t²) a. Find the length of the path on 0≤t≤1.…

A: Given,

Q: Find the positive t when the vector r(t) = (4t, 4t, 5t2 – 6) is perpendicular to r' (t). t =

A: We use the definition of the perpendicular of two vectors to find the positive value of t.

Q: Q2) if the vechrs V=-i +5 and ū=Tz i+5J+2 R Find a) The scalev component of ū in the divection of V…

A:

Q: solve for th e vector x in terms of the vectors a and b. x - a= 2(x - 2a)

A:

Q: (E) Let T : R + R? defined by T 2r1 + 2. Which of the following vectors dose not belong to the range…

A:

Q: Q5) Let f(x, y) = Find unit vector for which Duf(2,3) = 0. %3D x+y

A:

Q: Find a unit vector parallel to the tangent line of y = x at (2,8). What angle does this vector make…

A: Given that, y=x3   We have to find a unit vector parallel to the tangent line of the given curve at…

Q: Q1] Find a unit vector normal to the surface 3x2 у — узz? аt the point (1,-2, -1)

A:

Q: Find a vector equation for the line segment from (2, -4, 5) to (6, 4, 4). (Use the parameter t.)…

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

Q: c. For that sum vector c find the magnitude and angle with positive direction of x-axis of the…

A:

Q: find the distance d(u, v) between u and v in the given exercise.

A: We need to find the distance between the two vectors.

Q: 5) Consider the vector function r = (9 – 2t, 4 + 2t, vZt²) a. Find the length of the path on 0<t<1.…

A: Given vector function The length of the path is found by the formula Given interval is 0 to 1

Q: 2 Let u = = 1 (i) Find the angle between u and v. (ii) Find a vector w of length 2 in the direction…

A:

Q: 3 - Find the Derivatives of the following Vectors, Where F(t)* = 2secti – 3j* + csctk and G(t)* =…

A:

Q: F(t) = <뜻, X0t3/2 + 14, 9t-6) t? 2/6 %D

A:

Q: For time t> 0, the position of a particle moving in the xy-plane is given by the vector (, e3t) .…

A: Option e is true.

Q: e vector x²y?

A:

Q: find the distance d(u, v) between u and v in the given exercise.

A:

Q: Match the vector-valued function with its graph. r(u, v) = ui + vj + uvk -2-1 2 2

A:

Q: 7. For vectors a and b in R? prove Lagrange's identity: ||a x b|? = ||a|| ||b||? – (a · b)?

A: for vectors a and b in ℝ2 prove -lagrange's identity a×b2=a2b2-a·b2

Q: Q1:(A) What is the angle between the normal vectors to the curve F (1) = (2x² + x + 1)i + (+1)j +rk…

A:

Q: Find the domain of the vector function. (Enter your answer using interval notation.) r(t) = (V16 –…

A:

Q: Find the binormal vector for 7(t) = (3t, sint, cos t) А. ВО cost, sint V10 10 1 B(e) = (- 3 В. ВО)…

A:

Q: Q1A) The vectors A = 3i + j + 4k, B = 2i - 3j - k, find vector normal to A and In plane of A and, B.

A: Solution is given below:

Q: Q2) Find the vectors „N of the curve r(1) = ) at the point (1.1)

A:

Q: Using a convenient scale, find the resultant of the following vectors graphically: 10m at 40o with…

A: According to Polygon Law of forces, if a number of coplanar forces acing at a point is represented…

Q: H.W 9- Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b %3D %3D…

A: Given: a→=1,1, b→=-1,0 To find: A vector in the same direction as but a→+b→ five times as long.

Q: Find the positive t when the vector r(t) = (7t, 6t², 9t2 3) is perpendicular to r'(t). - t =

A: NOTE: Refresh your page if you can't see any equations. . take derivative

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: Evaluate /1+ x² + y²dS, where S is the helicoid with vector equation т(и, 0) - = 0 < u < 3, 0 < v <…

A:

Q: find the derivitive, r'(t), of the vector function.  r(t)=a+3tb+t^7c

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.