Q. 16 Let v0=a,聽b聽and let v=x,聽y聽D... [FREE SOLUTION]

Chapter 10: Q. 16 (page 801)

Let $v_{0} = (a, b)$ and let $v = (x, y)$ Describe the sets of points in $R^{2}$ satisfying the following properties:
$(a) . |v| = 4 (b) . |v| 鈮� 4 (c) . |v - v_{0}| = 4$

Short Answer

Expert verified

(a) The set of points are $(0, 4), (0, - 4), (4, 0) and (- 4, 0)$ etc.

(b) The set of values of $(x, y)$ , which satisfy the relation $x^{2} + y^{2} 鈮� 16$ will be the required set of points.

The set of points are role="math" localid="1663552322576" $(0, 1), (0, 2), (0, 3), (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (0, 4), (0, - 4), (2, 3) etc .$

(c) The set of values of $(x, y) and (a, b)$ , which satisfy the relation ${(x - a)}^{2} + {(y - b)}^{2} = 16$ will be the required set of points.

The set of points $(x, y)$ are role="math" localid="1663552768845" $(5, 1), (4, 1) and (1, 5) etc .$

The set of points $(a, b)$ arerole="math" localid="1663552801181" $(1, 1), (0, 1) etc$ .

Step by step solution

Part (a)

Given that, $v = (x, y)$

role="math" localid="1663552119670" $|v| = \sqrt{x^{2} + y^{2}}$

role="math" localid="1663552143759" $\sqrt{x^{2} + y^{2}} = 4 x^{2} + y^{2} = 16 (Squaring both side)$

When $x = 0$ ,

$y = \sqrt{16} y = 卤 4$

When $y = 0$ ,

$x = \sqrt{16} x = 卤 4$

Thus, the set of points are $(0, 4), (0, - 4), (4, 0) and (- 4, 0)$ etc.

Part (b)

Given that, $v = (x, y)$

$|v| = \sqrt{x^{2} + y^{2}}$

$\sqrt{x^{2} + y^{2}} 鈮� 4 x^{2} + y^{2} 鈮� 16 (Squaring both side)$

All the points that satisfy the above relationship, will be the required sets of points.

The set of points are,

$(0, 1), (0, 2), (0, 3), (1, 1), (1, 2), (1, 3), (2, 1), (2, 2), (3, 1), (0, 4), (0, - 4), (2, 3) etc .$

Part (c)

Given that,

v = (x, y) and v_{0} = (a, b) v - v_{0} = \{(x - a), (y - b)\} |v - v_{0}| = \sqrt{{(x - a)}^{2} + {(y - b)}^{2}} \sqrt{{(x - a)}^{2} + {(y - b)}^{2}} = 4 (Given) {(x - a)}^{2} + {(y - b)}^{2} = 16 (Squaring both side)

All the values of $(x, y) and (a, b)$ that satisfy the above relationship will be the required sets of points.

The values of $(x, y)$ are $(5, 1), (4, 1) and (1, 5) etc .$

The values of $(a, b)$ are $(1, 1), (0, 1) etc$ .

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91影视

Let $v_{0} = (a, b)$ and let $v = (x, y)$ Describe the sets of points in $R^{2}$ satisfying the following properties:
$(a) . |v| = 4 (b) . |v| 鈮� 4 (c) . |v - v_{0}| = 4$

Short Answer

Step by step solution

Part (a)

Part (b)

Part (c)

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91影视

Let v0=a,band let v=x,yDescribe the sets of points in R2 satisfying the following properties: (a).v=4(b).v鈮�4(c).v-v0=4

Short Answer

Step by step solution

Part (a)

Part (b)

Part (c)

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Let $v_{0} = (a, b)$ and let $v = (x, y)$ Describe the sets of points in $R^{2}$ satisfying the following properties:
$(a) . |v| = 4 (b) . |v| 鈮� 4 (c) . |v - v_{0}| = 4$