Solving Right Triangles with Pythagorean Theorem

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Questions and Answers

What is the expression for the vector sum of two vectors A and B?

𝐂 = (𝐀 𝐱 + 𝐁𝐱 )𝐢 + (𝐀 𝐲 + 𝐁𝐲 )𝐣 (correct)

𝐂 = (𝐀 𝐱 - 𝐁𝐱 )𝐢 + (𝐀 𝐲 - 𝐁𝐲 )𝐣

𝐂 = (𝐀 𝐱 × 𝐁𝐱 )𝐢 + (𝐀 𝐲 × 𝐁𝐲 )𝐣

𝐂 = (𝐀 𝐱 / 𝐁𝐱 )𝐢 + (𝐀 𝐲 / 𝐁𝐲 )𝐣

What is the expression for the vector A in terms of its components, if it does not lie in the x-y plane?

𝐀 = 𝐀 𝐱 𝐢 + 𝐀 𝐲 𝐣 + 𝐀𝐳 𝐤 (correct)

𝐀 = 𝐀 𝐱 𝐢 + 𝐀 𝐲 𝐣

𝐀 = 𝐀 𝐱 𝐢 × 𝐀 𝐲 𝐣

𝐀 = 𝐀 𝐱 𝐢 - 𝐀 𝐲 𝐣

What is the cross product of two vectors Ax, Ay, Az and Bx, By, Bz in terms of i, j, and k?

Ay Bz i + Az Bx j + Ax By k + Bx Ay k + By Az i + Bz Ax j

Ay Bz i - Az Bx j + Ax By k - Bx Ay k - By Az i - Bz Ax j (correct)

Ax By i + Ay Bz j + Az Bx k + Bx Ay i - By Az j - Bz Ax k

Ax Bz i - Ay Bx j + Az By k + Bx Az i - By Ax j - Bz Ay k

What is the formula used to find the direction of the resultant vector in a right triangle?

θ = Tan⁻¹ (a/b) Signup and view all the answers

Which direction is equivalent to 15° S of E?

75° E of S Signup and view all the answers

What is the scalar product of two vectors A and B, if the angle between them is 60°?

A ∙ B is positive Signup and view all the answers

Which method is used to find the resultant vector of two or more vectors that are non-collinear but coplanar?

The Polygon Method Signup and view all the answers

What is the geometric interpretation of the scalar product of two vectors A and B?

The cosine of the angle between A and B Signup and view all the answers

What is the direction of vector C in the given diagram?

30 km due west Signup and view all the answers

What is the formula used in the Pythagorean Theorem to find the magnitude of the resultant vector?

c² = a² + b² Signup and view all the answers

What is the resultant of the given vectors A, B, C, D, and E?

A - B - C - D - E Signup and view all the answers

What is the condition for the scalar product of two vectors A and B to be negative?

The angle between A and B is greater than 90° Signup and view all the answers

What is the value of C - D in the given diagram?

5 km due west Signup and view all the answers

What is the name of the law used to find the magnitude of the resultant vector when the triangle formed is not a right triangle?

Cosine Law Signup and view all the answers

What is the result of the vector sum of two vectors A and B, if A and B are perpendicular to each other?

The magnitude of the resultant vector is less than the sum of the magnitudes of A and B Signup and view all the answers

What is the expression for the vector sum of two vectors A and B, if A = 2𝐢 + 3𝐣 and B = 4𝐢 - 2𝐣?

𝐂 = 6𝐢 + 5𝐣 Signup and view all the answers

What is the first step in the Component Method?

Resolve the vectors into their x- and y-components Signup and view all the answers

What is the value of D - A - B in the given diagram?

35 km due west Signup and view all the answers

What is the purpose of the Polygon Method?

To find the resultant vector of two or more vectors that are non-collinear but coplanar Signup and view all the answers

What is the convention used for sign of vectors in the given diagram?

to the left is negative, to the right is positive Signup and view all the answers

What is the relationship between the scalar product of two vectors A and B, and the angle θ between them?

A ∙ B is proportional to cos(θ) Signup and view all the answers

What is the formula used in the Sine Law to find the magnitude of the resultant vector?

a / sin(A) = b / sin(B) = c / sin(C) Signup and view all the answers

Which of the following is a true statement about the given vectors?

A and D are in the same direction Signup and view all the answers

What is the last step in the Polygon Method?

Measure the magnitude of the resultant vector Signup and view all the answers

What is the main characteristic of non-contact forces?

They attract or repel from a distance Signup and view all the answers

What is mass?

The amount of matter contained in a body Signup and view all the answers

What is the direction of the weight of an object?

Downwards Signup and view all the answers

What is the formula for weight?

W = mg Signup and view all the answers

Why does the weight of a person vary on different planets?

Because of the planet's gravity Signup and view all the answers

What is an example of a field force?

Magnetic force Signup and view all the answers

What remains constant for an object, regardless of its location?

Its mass Signup and view all the answers

Where is the concentrated weight of an object considered to act?

At the center of gravity Signup and view all the answers

What is the significance of the statement 'he finds himself back where he started' in the given problem?

It means that the resultant of the four displacements is equal to zero. Signup and view all the answers

What is the direction of the vector B?

45o E of S Signup and view all the answers

What is the method used to solve for the fourth unmeasured displacement?

Component method Signup and view all the answers

What is the value of Dx in the given problem?

-108.4924 m Signup and view all the answers

What is the direction of the fourth displacement?

40.90o S of W Signup and view all the answers

What is the value of Dy in the given problem?

-93.9947 m Signup and view all the answers

What is the magnitude of the fourth displacement?

143.5465 m Signup and view all the answers

What is the equation used to calculate the magnitude of the fourth displacement?

D2 = Dx2 + Dy2 Signup and view all the answers

Study Notes

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Description

Solve for the magnitude and direction of the resultant using the Pythagorean Theorem and trigonometric identities in right triangles.