Question

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Topic: 3D .


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Answer 1

EXPLANATION.

Point on a line has co-ordinates.

⇒ (p + 1, p - 3, √2p).

P is any real number.

As we know that,

Co-ordinates = (p + 1, p - 3, √p) = (x, y, z).

⇒ x = p + 1.

⇒ x - 1 = p. - - - - - (1).

⇒ y = p - 3.

⇒ y + 3 = p. - - - - - (2).

⇒ z = √2p.

⇒ z - 0 = √2p. - - - - - (3).

As we know that,

Cartesian form : Equation of a straight line passing through a fixed point (x₁, y₁, z₁) and having direction ratios a, b, c is.

⇒ (x - x₁)/a = (y - y₁)/b = (z - z₁)/c.

Put the values in the equation, we get.

⇒ (x - 1)/1 = (y + 3)/1 = (z - 0)/√2

Ratios of direction = 1, 1, √2.

Direction cosines of the line = 1/2, 1/2, 1/√2.

Option [A] is correct answer.

                                                                                                                       

MORE INFORMATION.

Equation of line.

(1) = Vector form = Equation of line passes through A($\vec{a}$) and parallel to vector ($\vec{b}$) is,

$\implies \vec{r} = \vec{a} + \lambda \vec{b}$