Mathematics: Use the equation a = iaiâ to express each of the following vectors as the product of its magnitude and (unit vector) direction. (your instructors prefer angle bracket notation for vectors.) (a) (2, 1, -3) (b) 2i - 3j + 4k (c) the sum of (1, 2, -3) and (2, 4, 1)

Use the equation a = iaiâ to express each of the

Ответ:

Usman458

02.01.2022

Mathematics

a) $\:\:=\sqrt{14}\cdot \frac{\:\:}{\sqrt{14} }$

b) $\:\:=\sqrt{29} \cdot \frac{\:\:}{\sqrt{29} }$

c) $\:\:=7\cdot \frac{\:\:}{7}$

Step-by-step explanation:

a) Let a=<2,1,-3>

The magnitude of a is $|a|=\sqrt{2^2+1^2+(-3)^2}$

$|a|=\sqrt{4+1+9}=\sqrt{14}$

The unit vector in the direction of a is

$\hat{a}=\frac{\:\:}{\sqrt{14} }$

Using the relation $a=|a|\hat{a}$ , we have

$\:\:=\sqrt{14}\cdot \frac{\:\:}{\sqrt{14} }$

b) Let a=2i - 3j + 4k

$|a|=\sqrt{2^2+(-3)^2+4^2}$

$|a|=\sqrt{4+9+16}=\sqrt{29}$

$\hat{a}=\frac{\:\:}{\sqrt{29} }$

Using the relation $a=|a|\hat{a}$ , we have

$\:\:=\sqrt{29} \cdot \frac{\:\:}{\sqrt{29} }$

c) Let us first find the sum of <1, 2, -3> and <2, 4, 1> to get:

<1+2, 2+4, -3+1>=<3, 6, -2>

Let a=<3, 6, -2>

The magnitude is

$|a|=\sqrt{3^2+6^2+(-2)^2}$

$|a|=\sqrt{9+36+4}=\sqrt{49}=7$

The unit vector in the direction of a is

$\hat{a}=\frac{\:\:}{7}$

Using the relation $a=|a|\hat{a}$ , we have

$\:\:=7\cdot \frac{\:\:}{7}$

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Ответ:

monyeemonyee12

14.09.2022

Mathematics

Step-by-step explanation:two pairs of opposite sides parallel. ...

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two pairs of opposite angles congruent. ...

one angle is supplementary to both consecutive angles. ...

Diagonals bisect each other.

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Use the equation a = iaiâ
to express each of the following vectors as the product of its magnitude and (unit vector) direction. (your instructors prefer angle bracket notation < > for vectors.)
(a) (2, 1, -3)
(b) 2i - 3j + 4k
(c) the sum of (1, 2, -3) and (2, 4, 1)

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Use the equation a = iaiâ to express each of the following vectors as the product of its magnitude and (unit vector) direction. (your instructors prefer angle bracket notation < > for vectors.) (a) (2, 1, -3) (b) 2i - 3j + 4k (c) the sum of (1, 2, -3) and (2, 4, 1)

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Answers on questions: Mathematics

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Use the equation a = iaiâ
to express each of the following vectors as the product of its magnitude and (unit vector) direction. (your instructors prefer angle bracket notation < > for vectors.)
(a) (2, 1, -3)
(b) 2i - 3j + 4k
(c) the sum of (1, 2, -3) and (2, 4, 1)