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Applications of Cross Product

If x≠ 0,y≠ ...

Question

If $x \neq 0, y \neq 0, z \neq 0$ and $∣ ∣ ∣ ∣ \begin{matrix} 1 + x & 1 & 1 1 + y & 1 + 2 y & 1 1 + z & 1 + z & 1 + 3 z \end{matrix} ∣ ∣ ∣ ∣ = 0$ then $x^{- 1} + y^{- 1} + z^{- 1}$ is equal to

A

- 1

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B

- 2

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C

- 3

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D

none of these

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Solution

The correct option is C $- 3$

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Similar questions

x, y, z

are non-zero real numbers and

∣ ∣ ∣ ∣ \begin{matrix} 1 + x & 1 & 1 1 + y & 1 + 2 y & 1 1 + z & 1 + z & 1 + 3 z \end{matrix} ∣ ∣ ∣ ∣ = 0

- (\frac{1}{x} + \frac{1}{y} + \frac{1}{z})

is equal to________

The line $\frac{x - x_{1}}{0} = \frac{y - y_{1}}{1} = \frac{z - z_{1}}{2}$ is:

For complex numbers

z_{1} = x_{1} + i y_{1}

z_{2} = x_{2} + i y_{2}

z_{1} \cap z_{2}

x_{1} \leq x_{2}

y_{1} \leq y_{2}

. Then, for all complex numbers

z

1 \cap z

\frac{1 - z}{1 + z} \cap 0

x^{2} + y^{2} \geq 0

y \geq 0

.If true enter 1 else 0.

Q. The plane through the intersection of the planes

x + 2 y + z - 1 = 0

2 x + y + 3 z - 2 = 0

is perpendicular to the planes

x + y + z - 1 = 0

x + k y + 3 z - 1 = 0

. Then the value of

k

x

y

z

> 0

and are not equal to

1

log x + log y + log z = 0

. What is the value of

x^{\frac{1}{log y} + \frac{1}{log z}} \times y^{\frac{1}{log z} + \frac{1}{log x}} \times z^{\frac{1}{log x} + \frac{1}{log y}}

.
(All log functions have base

10

)

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