The two variable vectors $3x\widehat{\dot{\mathbf{i}}} + y\widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}}$ and $x\widehat{\dot{\mathbf{i}}} - 4\ y\ \widehat{\dot{\mathbf{j}}} + 4\ \widehat{\mathbf{k}}$ are orthogonal to each other, then the locus of $(x,y)$is

Question

Dr. Abubacker · Accepted Answer

(a)
Given vectors are orthogonal.
$	herefore(3x\widehat{\dot{\mathbf{i}}} + y\widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}}$)∙$\left( x\widehat{\dot{\mathbf{i}}} - 4y\widehat{\dot{\mathbf{j}}} + 4\widehat{\mathbf{k}} ight) = 0$
$\Longrightarrow \ {3x}^{2} - 4y^{2} - 12 = 0$
$\Longrightarrow \ \frac{x^{2}}{4} - \frac{y^{2}}{3} = 1$
Hence, it represent a hyperbola.

Q. The two variable vectors $3x\widehat{\dot{\mathbf{i}}} + y\widehat{\dot{\mathbf{j}}} - 3\widehat{\mathbf{k}}$ and $x\widehat{\dot{\mathbf{i}}} - 4\ y\ \widehat{\dot{\mathbf{j}}} + 4\ \widehat{\mathbf{k}}$ are orthogonal to each other, then the locus of $(x,y)$is

Explanation

Reviewed by Dr. Abubacker

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