152 Answered Questions for the topic Vectors


Find boat's true speed and heading?

A small boat leaves the dock at Camp DuNuthin and heads across the Nessie River at 18 miles per hour, relative to the water, at a bearing of S61° W . The river is flowing due east at 6 miles per... more


Trig question on bearing of a plane using vectors

A plane is heading due south with an airspeed of 211 mph. A wind from a direction of 53 degrees is blowing at 17 mph. Find the bearing of the plane.


Verification of Stokes Theorem

Could someone explain how do we verify stokes theorem for the vector field F=zi + (2x+z)j + xk taken over the triangular surface S in the plane (x/1)+(y/2)+(z/3)=1 bounded by the planes x=0 y=0 and... more


Spherical and cylindrical polar coordinates

How do we diffentiate in between when to use spherical polar coordinates and cylindrical polar coordinates for a transformation in a vector calculus question(line integral, stokes theorem etc.)


Equation of a plane

How do we fins the equation of the line through (-1,3,2) and perpendicular to the plane x+2y+2z=3, the length of the perpendicular and the coordinates of the foot


HELP! Vectors - collision

Two boats, A and B, are moving in straight lines and the position of each particle after t seconds is given by the following equations: 𝒓𝐴 = 2𝑡𝒊 + (30 − 𝑡)𝒋 𝒓𝐵 = 2𝑡𝒊 + 60𝒋 − 4𝑡𝒋 (a) Find the... more


Help me! Math Vectors! A helicopter wishes to fly directly East at 100 km/h.

A helicopter wishes to fly directly East at 100 km/h. If a constant wind blows directly from the North-East at 40 km/h, find the direction and velocity of the wind speed that must be maintained in... more


Vectors - lines and equations

1) How do we find the perpendicular distance of a point C=c fron the straight line (r-a)^b =02) how do we find the shortest distance between the two skew lines (r-a)^b =0 and (r-c)^d =0


Physics, Vectors and resultant vectors

1) A dog is on a street chasing cars. He runs 30m west and stops. He then chases another car 20m north before chasing the mailman 60m East...a) What is the dogs distance traveled?..b) What is the... more


vectors and velocity

an airplane is taking off headed due north with an air speed of 173mph at an angle of 18\deg relative to the horizontal. the wind is blowing with a velocity of 42 miles per hour at an able of... more


Where am I confused about force addition?

As far as my knowledge is concerned, a vector quantity should possess magnitude and direction & more over it should also obey the laws of vector addition. As we all know that the vector sum of... more


Torque direction meaning?

I apologize if this question is dumb, but I've looked all over for a straightforward answer and either I can't find one or the terms are too complex for me to understand. I have only a rudimentary... more


Understanding the trajectory of a projectile?

It is stated that a projectile's motion can be divided into individual vectors. Now according to the laws of physics, the forces acting in the y-direction will never cancel or affect the force... more



A block slides 42 m down a ramp that makes an angle of 60 degrees with the ground. Determine the mass of the block if 10 400 J of work was done. (Assume 1 kg exerts a force of 9.8 N).


What is an orthogonal vector to (4, 2)?


Two canoeists are paddling a canoe. Vector analysis

Two canoeists are paddling on opposite sides of a canoe. One extends her arms out so that the force of 15lbs she exerts is directed backwards at an angle of 22 degrees with the canoe. The other... more
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