If vector a=(x,2,-6) and vector b=(1,-1,-6) and a=b find the value of x?

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If vector a=(x,2,-6) and vector b=(1,-1,-6) and a=b find the value of x?

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Answer 1 · 2018-04-01T23:31:28

$x = \sqrt{2} i$ $x = sqrt(2)i$

Explanation:

The formula for the magnitude of a vector can be used to solve for $x$ $x$ :

vector magnitude: $\sqrt{x^{2} + y^{2} + z^{2}}$ $sqrt(x^{2}+y^{2}+z^{2})$

Since the magnitude of $\to a$ $vec{a}$ is equal to the magnitude of $\to b$ $vec{b}$ :
$a = b$ $a = b$
$\sqrt{x^{2} + {(2)}^{2} + {(- 6)}^{2}} = \sqrt{{(1)}^{2} + {(- 1)}^{2} + {(- 6)}^{2}}$ $sqrt(x^{2}+(2)^{2}+(-6)^{2}) = sqrt((1)^{2}+(-1)^{2}+(-6)^{2})$
$x^{2} + {(2)}^{2} + {(- 6)}^{2} = {(1)}^{2} + {(- 1)}^{2} + {(- 6)}^{2}$ $x^{2}+(2)^{2}+(-6)^{2} = (1)^{2}+(-1)^{2}+(-6)^{2}$
$x^{2} + 4 + 36 = 1 + 1 + 36$ $x^{2}+4+36 = 1+1+36$
$x^{2} + 40 = 38$ $x^{2}+40 = 38$
$x^{2} = - 2$ $x^{2} = -2$
$x = \sqrt{- 2}$ $x = sqrt(-2)$
$x = \sqrt{2} i$ $x = sqrt(2)i$

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If vector a=(x,2,-6) and vector b=(1,-1,-6) and a=b find the value of x?

1 Answer

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