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Precalculus Mathematics for Calculus

James Stewart, Lothar Redlin, Saleem Watson

$Math Studyset Vaia Explanations$ Math

7th Edition · 948 pages

ISBN: 9781337067508

Chapter 9: Q3. (page 637)

Sketch the vector indicated. (The vectors u and v are shown in the figure.)

Short Answer

Expert verified

The sketch of the vector $2 u = <- 4, 6>$

Step by step solution

Step 1. Identifying the coordinates of the points.

The coordinates of the head of the vector is $\begin{array}{l} u = 〈- 2, 3〉 \\ v = 〈3, 4〉 \end{array}$

Step 2. Applying the operations.

$2 u = 2 <- 2, 3>$

$= <2 (- 2), 2 (3)>$

$= <- 4, 6>$

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Most popular questions from this chapter

True Velocity of a Jet

A jet is flying through a wind that is blowing with a speed of $55 m i / h$ in the direction $N 30^{°} E$ (see the figure). The jet has a speed of $765 m i / h$ relative to the air, and the pilot heads the jet in the direction $N 45^{°} E$ .

(a) Express the velocity of the wind as a vector in component form.

(b) Express the velocity of the jet relative to the air as a vector in component form.

(d) Find the true speed and direction of the jet.

Express the vector with initial point Pand terminal point Qin component form.

The forces $F_{1}, F_{2}, F_{3} . . . . . . . F_{n}$ acting at the same point Pare said to be in equilibrium if theresultant force is zero,

a) the resultant forces acting at P, and.

b) the additional force

required (if any) for the forces to be in equilibrium.

$F_{1} = i - j, F_{2} = i + j, F_{3} = - 2 i + j$

Operations with Vectors Find, $2 u,$ $- 3 v$ $, u + v$ and $3 u - 4 v$ for the given vectors $u$ and $v$ .

$u = ⟨ 0, - 1 ⟩, v = ⟨ - 2, 0 ⟩$ .

Determine Dot products and angle between vectors.

a) $u \cdot v$

b) The angle between u and v to the nearest degree.

$u = - 5 j, v = - i - \sqrt{3} j$

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Sketch the vector indicated. (The vectors u and v are shown in the figure.)

Short Answer

Step by step solution

Step 1. Identifying the coordinates of the points.

Step 2. Applying the operations.

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Most popular questions from this chapter

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