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208 Answered Questions for the topic Vectors


Vector Angles in Radians

Compute the angle in radians between each of the following vectors:a) v = (-2, -2) and w = (2, -2)b) v = (5, 0, 5) and w = (2, 2, 0)c) v = (3, 3, 3, 3) and w = (0, 0, -1, -1)


Vector Question

A rectangle R3 has three of its corners at the points (3,1,1), (2,3,4) and (1,1,2). What are the coordinates of its fourth corner?


Vectors: True or False Questions

Determine which of the following statements are true and which are false.(a) There exist vectors v, w ∈ R3 such that ||v|| = 3, ||w|| = 3, and ||v + w|| = 7.(b) There exist vectors v, w ∈ R2 such... more
Vectors Linear Algebra


Vectors: Solve the following equations for the vector x ∈ ℝ2

x ∈ ℝ2(a) −2x + (0, −1) = (−2, 1) (b) (−4, 0) − x = (1, −1) − 2x (c) 2(x + 2(x + 2x)) = 5(x + 5(x + 5x)


Vectors: Determine which of the following statements are true and which are false.

(a) For vectors v, w, z ∈ ℝn , if v + w = v + z then w = z. (b) The vector (3, 2, 1) is a linear combination of the vectors (1, 1, 1) and (1, 1, 0). (c) For vectors v, w, z ∈ ℝn, if v · w = v · z,... more


Vector Parallelogram Question

If a parallelogram has diagonals described by the vectors x = (5, 4) and y = (3, −2), what are the sides v and w of that parallelogram?
Vectors Math Trigonometry


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
Vectors Trigonometry


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.
Vectors Calculus Theorems


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
Vectors Calculus Geometry


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.)
Vectors Calculus Geometry


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
Vectors Linear Algebra


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
Vectors Linear Algebra


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 Physics


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
Vectors Physics Forces


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
Vectors Physics Forces


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
Vectors Physics Forces


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
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