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Chapter 10: Q. 10 (page 800)

How do you subtract two vectors algebraically? Geometrically

Short Answer

Expert verified

$u = x_{1} i + y_{1} j and v = x_{2} i + y_{2} j \vec{u} - \vec{v} = (x_{1} - x_{2}) i + (y_{1} - y_{2})$

Step by step solution

01

Subtract two vectors algebraically

Let two vectors are,

$u = x_{1} i + y_{1} j and v = x_{2} i + y_{2} j \vec{u} - \vec{v} = (x_{1} - x_{2}) i + (y_{1} - y_{2})$

Example:

role="math" localid="1663308079530" $\vec{u} = 3 i + 8 j and \vec{v} = 2 i - 4 j \vec{u} - \vec{v} = (3 i - 2 i) + (8 j + 4 j) = i + 12 j$

02

Subtract two vectors geometrically

To subtract two vectors geometrically we position their initial points together, as we see in the right-hand figure. The vector $u - v$ extends from the terminal point of v to the terminal point of u.

Example:

localid="1663308270938" $\vec{u} = 3 i + 8 j and \vec{v} = 2 i - 4 j \vec{u} - \vec{v} = (3 i - 2 i) + (8 j + 4 j) = i + 12 j$

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Most popular questions from this chapter

In Exercises 20-23, find the dot product of the given pairs of vectors and the angle between the two vectors.

$u = <- 5, 1, 3>, v = <- 3, 2, 7>$

Prove the first part of Theorem $1.31$ (a): If $k > 0$ , then $\lim_{x \to \infty} x^{k} = \infty$ . (Hint: Given $M > 0$ , choose $N = M^{1 / k}$ . Then show that for $x > N$ it must follow that $x^{k} > M$ .)

Calculate each of the limits:

$\lim_{h \to 0} \frac{\frac{1}{1 + h} - 1}{h}$ .

In Exercises 24-27, find ${comp}_{u} v, {proj}_{u} v$ and the component of v orthogonal tou.

role="math" localid="1649693816584" $u = <3, 1, - 2>, v = <- 6, - 2, 4>$

If u, v and w are three vectors in $ℝ^{3}$ , what is wrong with the expression $u \times v \times w$ ?

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