252 Answered Questions for the topic Vectors

05/27/22

How would I answer the following vectors questions?

is it possible to have a↓b undefined? is it possible to have a↓b = b↓a? explain why a↓c = a↓(b↓c)? * all of a,b and c should have the arrow above them but I couldn’t find a way to add it *
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05/22/22

Calculus Question
Please answer the following questions and show all steps. Thank you in advance. Given the points X(0, 2, –1), Y(3, 1, 2), and Z(–3, 2, 5), find (Vector XY × Vector XZ) • Vector YZ. If vector b =... more
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03/30/22

Dot product problem
a*b=|a||b|cosθ; |a|=1, |b|=4, θ=π/3Find: 1) (2a-3b)(a+b)2) |2a-3b|How to solve these kind of problems?
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03/30/22

Vector dot product problem
a*b=|a||b|cosθIt is known that |a|=1, a*b=-2a) find θ, if |b|=2b) find the interval of |b|
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Vectors Trigonometry

02/22/22

Application of Vectors
 A boat heads directly north across a river 68 m wide at a rate of 3 m/s. The current is flowing downstream (due west) at 1.9 m/s.A) What is the resultant velocity of the boat? What is the... more
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12/02/21

A hot air balloon is rising vertically 4m/s while the wind is blowing horizontally at 3m/s. Find the speed v of the balloon and the angle Θ it makes with the horizontal.

The balloons speed is _____________  m/s, and it is rising at an angle of ___________ degrees to the horizontal. 
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07/29/21

Let →a = <−4,−2,−3> and →b= <−2,0,−5>. Find (−2→a) − (2→b).
Let →a = <−4,−2,−3> and →b= <−2,0,−5>. Find (−2→a) − (2→b).<___ , ___ , ___>
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Vectors Calculus Vector

07/28/21

Determine the Cartesian equation of the plane that passes through the points (1, 4, 5) and (3, 2, 1) and is parallel to the plane 2x – y + z + 1 = 0.
Determine the Cartesian equation of the plane that passes through the points (1, 4, 5) and (3, 2, 1) and is parallel to the plane 2x – y + z + 1 = 0.
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Vectors Calculus Velocity

07/22/21

An airplane is flying north with an airspeed of 350 km/h. Find the resultant ground velocity when the plane encounters a wind blowing at 60km/h from the south east.
An airplane is flying north with an airspeed of 350 km/h. Find the resultant ground velocity when the plane encounters a wind blowing at 60km/h from the south east.
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Vectors Physics Mechanics

07/20/21

Basic problem on force vectors
Two equal forces with magnitude F act on a box by an angle of 120 degrees. Find the magnitude of the resultant force.(The answer is F)
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06/20/21

Vectors, Linear Map; Injective and surjective
Let vector, v = - j + k in R3f : R3 ---> R3f(u) = v x u + 2u for u in R3 (u, v, j, k are vectors)How can we determine if f is surjective or not? How can we determine if f is... more
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06/20/21

Vectors, Linear Map; Injective and surjective
Let vector, v = - j + k in R3f : R3 ---> R3f(u) = v x u + 2u for u in R3 (u, v, j, k are vectors)How can we determine if f is surjective or not? How can we determine if f is... more
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06/15/21

I need help with 2 calc-related-questions.

Determine the value of k such that u and v are orthogonal. u = [2, k, -1] and v = [3, -2, 7] Determine the value(s) of k such that (2k, 3, k+1) x (k-1, k, 1 = (1, -2, 2) The x stands as a tip to... more
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Vectors Calculus Planes

06/14/21

determine the line of intersection (in parametric form) of the following planes.
The direction vector within you line must be stated without fractions Line1: 3x -y + 2z = 4 Line2: 6x + 2y - z = 3
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06/09/21

geometric and cartesian vectors
(a) A fishing boat sets its course at a heading of S70°W, with a speed of 30 knots. The water current is flowing from a bearing of S60°E, at 7 knots. Determine the resultant velocity of the fishing... more
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06/08/21

Perpendicular Vectors
Determine a value of t so that vector u = [9,t] and vector v = [-16,t] are perpendicular.-Also, are projections of perpendicular vectors always 0? A friend stated that they were but that doesn't... more
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Vectors Math Mathematics

06/08/21

Calculate angle DEF

Triangle DEF has vertices D(-3,5), E(2,3) and F(6,7). Calculate angle DEF. 
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05/27/21

Free Body Diagrams and Vectors
A student exerts a force of 72.0 N along the handle of a 196 N (gravitational force) lawn mower to push itacross the lawn at an angle of 39° with the horizontal.a)Draw a free-body diagram to... more
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Vectors Precalculus

05/17/21

For each of the following problems, sketch the vectors involved on a coordinate plane, then decompose vector into two vectors →v₁ and →v₂, where →v₁ is parallel to →w, and →v₂ is orthogonal to →w.
→v=- →i+6→j →w=3→i-2→j
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04/23/21

If u(t) = sin(6t), cos(6t), t and v(t) = t, cos(6t), sin(6t) , find d dt u(t) × v(t) .
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04/21/21

Find two vectors in opposite directions that are orthogonal to the vector u. (There are many correct answers)
u= 1/3i-3/8jVector in quadrant Iv=Vector in Quadrant IIIv=
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04/19/21

what is the resultant.

A bird is travelling at 150 km/h towards a true bearing of 300 . During its flight, the bird encounters a wind that is blowing towards a true bearing of 070 at 40 km/h. Determine the resultant... more
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04/12/21

Convert the following direction into desired one requested in each case.
 a) Polar coordinate (3km/h (fraction form), 60o), convert into both true and quadrant bearing. b) Scalar component (-5, -10), convert into polar coordinate and true bearing.
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Vectors Math Calculus

04/10/21

Calculus Question
Find (if possible) y and ß such that (all letters with arrows on top symbol (vectors)) c = ya + ßb where a = (2,0,-3), b = (0,-3,4) and c = (-6,6,1).
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Vectors Math Calculus

04/09/21

Calculus Questions (Vectors)

Find (if possible) y and ß such that (all letters with arrows on top symbol (vectors)) c = ya + ßb where a = (2,0,-3), b = (0,-3,4) and c = (-6,6,1). 
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