249 Answered Questions for the topic Vectors

Vectors Calculus

9d

#### In the diagram below, ABCD is a parallelogram, and E is the intersection point of the diagonals AC and BD. Name a single vector equivalent to each of the following:

https://www.bartleby.com/questions-and-answers/in-the-diagram-below-abcd-is-a-parallelogram-and-e-is-the-intersection-point-of-the-diagonals-ac-and/92570a4b-2b2d-45c0-8050-2e541a5e43ffAbove is the...
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#### 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?

#### 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|

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...
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#### 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.

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).<___ , ___ , ___>

#### 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.

#### 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.

#### 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)

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...
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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...
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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...
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#### 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

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...
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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...
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06/08/21

#### Calculate angle DEF

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

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...
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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

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=

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...
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#### 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.

#### 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).

#### 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).

#### Consider the vectors a = 2i + 4j - 6k,b = -3i + k, and c = 3j - 2k.

Consider the vectors (all letters should have arrows on top) a = 2i + 4j - 6k,b = -3i + k, and c = 3j - 2k.Please help with this Vectors Question, thank you.a) find the magnitude of the vector a....
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