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Chapter 10: Q. 9 (page 800)

How do you add 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

Addition of vectors algebraically

If two vectors $\vec{u} and \vec{v}$ are given,

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

Example:

$\vec{u} = 3 i + 8 j and \vec{v} = 2 i - 4 j \vec{u} + \vec{v} = (3 i + 2 i) + (8 j - 4 j) = 5 i + 4 j$

02

Addition of vectors geometrically

Let,

$\vec{u} = 3 i + 8 j and \vec{v} = 2 i - 4 j \vec{u} + \vec{v} = (3 i + 2 i) + (8 j - 4 j) = 5 i + 4 j$

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Most popular questions from this chapter

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

localid="1649405204459" role="math" $(u \times v) \cdot w and u \cdot (v \times w)$

In Exercises 36–41 use the given sets of points to find:

(a) A nonzero vector N perpendicular to the plane determined by the points.

(b) Two unit vectors perpendicular to the plane determined by the points.

(c) The area of the triangle determined by the points.

$P (2, - 5, 1), Q (- 4, 5, 8), R (- 1, - 5, 3)$

Find $u + v$ and $u - v$ . Also sketch $u, v, u + v$ and $u - v$ .

role="math" localid="1649578020551" $u = (3, - 4) a n d v = (- 1, 5)$

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

$v \times w and w \times v$

In Exercises 22–29 compute the indicated quantities when $u = (2, 1, - 3), v = (4, 0, 1), and w = (- 2, 6, 5)$

Find the volume of the parallelepiped determined by vectors u, v and w. Do u, v and w form a right-handed triple?

See all solutions

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