A force F = (6 + m)î – (3 + n)j – k passes through the point B whose position vector is b = î - (4 + m)j + k. Determine the vector moment, M, of F about the point %3D A with the position vector a = -î – 3j + (5 + n)k . Also find the angle in between.

Q: Find the velocity and acceleration vectors in terms of u, and u. r= a(9 + sin t) and 0 = 3 - e ',…

A: we derivative to find velocity and acceleration

Q: Find the acceleration vector for the position vector r(t) = (sin(5t), 6t", e "). x component = y…

A:

Q: Evaluate F. dS , where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 1, 0 < v<T…

A: since, y,-x,z3 and, ru,v=u cosv, u sinv,v So, F⇀ru,v=u cosv,-u sinv, v3 Now the normal upward vector…

Q: Find the work done by a force F = 4i + 9j (in N) in moving an object in a straight line from point…

A: Given:           F=4i+9j

Q: The vector equation for the curve of intersection of the surfaces a = y? and z = y in terms of the…

A:

Q: Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The…

A: Given:

Q: The wind is blowing at 20 miles per hour in the direction N30°W. Express its velocity as a vector v…

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

Q: Find the velocity and acceleration vectors in terms of u, and ug- de r= 5e a0 and = 1 dt v-Du, +Duo

A:

Q: The jet stream is blowing at 60 miles per hour in the direction N45°E. Express its velocity as a…

A: The jet stream is blowing at 60 miles per hour in the direction N45°E We need to express its…

Q: Evaluate /| F - d5 , where F = and S is the helicoid with vector equation r(u, v) 0 < u < 4, 0 < v…

A:

Q: Evaluate F.dS, where F = and S is the helicoid with vector equation r(u, v) = 0 < u < 3, 0 < v < T…

A: Given that, F¯=y,-x,z5 and ru,v=u cos v, u sin v, v where 0≤u≤3 and 0≤v≤π. Find ru×rv as follows.…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A:

Q: A force F = 61 – 3j – R passes through the point B whose position vector is b = î - 4j + R.…

A:

Q: Find a vector parametrization 7 (t) for the intersection between the two surfaces: x² + 10y4 + 223 =…

A: According to the given information, it is required to find a vector parametrization for the…

Q: Find the velocity and acceleration vectors in terms of u, and ug- de r=a cos 20 and == 5t, where a…

A:

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(: OS…

A:

Q: if A=i+j+X, B=zi-j+3ksfind vector normal to B and in plane of A and B- ans. $2(3i+9j+x)

A:

Q: Evaluate :// F. d5 , where F = and S is the helicoid with vector equation r(u, v) upward…

A:

Q: Evaluate F· dS , where F = and S is the helicoid with vector equation r(u, v) upward orientation.…

A:

Q: Find the postion vector R(t) given the velocity V(t)=(2t+2)i + 2sin(2t)j + 4t^3k and the initial…

A:

Q: Find the velocity and acceleration vectors in terms of u, and ug- r= 5 sint and 0 = 5t = (Du, + ()…

A: Recall:The velocity is given by      v =r' ur +(rθ') uθandThe accerleration is given by     a…

Q: A particle moves so that its position vector r at timet is r = a cos wt + bsin wt, where w is a…

A:

Q: D. Find the Iimit of the vector position r(t) = e "i+ j+ cos 2t k when t=0

A:

Q: Determine a direction derived from the point P and in the direction of the versor vector → informed…

A: Given:  Let f be a differentiable function at the point (a, b). Then f has a directional derivative…

Q: Let the velocity vector be v(t) = (2 cos(t), 5t“, 12 exp(3t)) and the initial position vector be…

A:

Q: di vergen a of the vector funchion v = xi+ 29j+ 32k, is Jhe 2

A:

Q: Find the acceleration vector for the position vector r(t) = (sin(11t), 4tº, e -2t). x component = y…

A: We need to find acceleration vector.

Q: Find a vector tangent to the curve of intersection of the two cyclinders x² + y? = 2 and y? + z² = 2…

A: To find a vector tangent to the curve of intersection of two cylinders        x2+y2=2 and…

Q: A velocity vector of v = 3t²i – 6t³ j – 4k L is governing the movement of an object in the 3D space.…

A:

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (cos(3t), cos(t), sin(t)) when…

A:

Q: Find the projection vector of the force F = 2 i + 3 j onto the line between the points A(3,4) and…

A: The given problem is solved below in detail.

Q: Find the work done by the force F = 7i − 9j in moving an object from the point  (8, 8)  to the…

A: Work done= Force X Displacement

Q: Find the work done by the force F= 6i – 2j in moving an object from the point (1, 7) to the point…

A: Work done by force F→ in moving object from point P to point Q is given by F→.PQ→ , where PQ→ = OQ→…

Q: Find the velocity and acceleration vectors in terms of u, and ue. r=7 sin 3t and 0= 9t 3Du, +ue V =…

A: Given To determine  the velocity and acceleration vectors

Q: Evaluate /| F. d5 , where F = and S is the helicoid with - vector equation r(u, v) = 0 < u < 1, 0…

A: To evaluate the below vector surface integral. ∫∫SF⋅dS

Q: The divergence of a vector D for rectangular coordinate is equal to [1/p / dp (pDp)] + [1/p Dø/dø]+…

A: We have to find divergence in rectangular coordinate

Q: A body is spiraling upward due to rapidly rising air on a path similar to that of a helix and having…

A: Consider the position vector.

Q: The unit vector normal to the plane 2x + 3y + 6z = 7 is

A: The given plane is 2x + 3y + 6z=7. The unit normal vector to fx,y is defined as n=∇F∇F. The normal…

Q: Find the velocity and acceleration vectors in terms of u, and ue. do a0 r= 9 e and :3 dt v=Ju, +Jue…

A:

Q: Evaluate F. dS, where F = and S is the helicoid with vector equation r(u, v) , 0 < u < 3, 0 < v <…

A: Given the vector field F→=y,-x,z2 and the surface S is parametrized as ru,v=ucosv,usinv,v,…

Q: The unit vector tangent to the curve r(t) = (1,41*,3r*) is (a) (0,4/5,3/5). (b) (0,81,6t)

A:

Q: Find the velocity and acceleration vectors in terms of u, and ug- de a0 r= 5 e and = 1 - dt v=Ju,…

A:

Q: |A force F = 9i + 8j – 4k is applied to a spacecraft with velocity vector v = 2i – 7j. Express F as…

A:

Q: The magnitude of the torque t developed by applying a force F at a point with position vector r at…

A: First we have to complete the required step by using the correct expression for torque.

Q: Sketch the curve of the vector function r(f) = ti +4costj, and indicate the orientation of the…

A: We have to sketch the curve of the vector function rt=ti+4costj, and to indicate the orientation of…

Q: Evaluate /| F · dS , where F = and S is the helicoid with vector equation S r(u, v) 0<u < 1, 0 <…

A:

Q: Find the velocity and acceleration vectors in terms of u, and ug. do r= 6 e a0 and -= 3 dt Ju, +Juo

A:

Q: Find the vector projection of a force F = 5i + 2j onto v = i - 3j and the scalar component of F in…

A: The force F=5i+2j onto v=i-3j Scalar component.Let a and b be two vectors, scalar projection of the…

Q: Evaluate F. dS, where F = and S is the helicoid with vector equation r(u, v) = 0< u < 2, 0 < v <…

A:

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.