JEE MATHEMATICS MCQ: DCS AND DRS

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Application +4 | -1

Let

{P}({x}, {y}, {z})

be a point in the first octant, whose projection in the

x y

-plane is the point

{Q}

. Let

{OP}=\gamma

; the angle between

{OQ}

and the positive

x

-axis be

\theta

; and the angle between OP and the positive

{z}

-axis be

\phi

, where

{O}

is the origin. Then the distance of

{P}

from the

{x}

-axis is:

View answer and explanation

Correct option: A

\gamma \sqrt{1-\sin ^2 \phi \cos ^2 \theta}

Option A (

\gamma \sqrt{1-\sin ^2 \phi \cos ^2 \theta}

) is correct because by using the given information and trigonometric relations, we can express the distance of P from the x-axis in terms of

\gamma

\theta

, and

\phi

More Questions from DCS AND DRS

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If the line

\frac{2-x}{3}=\frac{3 y-2}{4 \lambda+1}=4-z

makes a right angle with the line

\frac{x+3}{3 \mu}=\frac{1-2 y}{6}=\frac{5-z}{7},

then

4 \lambda+9 \mu

is equal to: The shortest distance between the lines

\frac{x}{2}=\frac{y}{2}=\frac{z}{1}

and

\frac{x+2}{-1}=\frac{y-4}{8}=\frac{z-5}{4}

lies in the interval :
A uniform rod,

4 {~m}

in length and weight

2 {~kg}

turns freely about a point distant one metre from one end and from that end a weight of

10 {~kg}

is suspended. The weight that must be placed at the other end to produce equilibrium is A line makes angles of

45^{\circ}

and

60^{\circ}

with the positive axes of

X

and

Y

respectively. The angle made by the same line with the positive axis of

Z

, is. The direction cosines of a line segment

\mathrm{AB}

are

-2 / \sqrt{17}

3 / \sqrt{17},-2 / \sqrt{17}

\mathrm{AB}=\sqrt{17}

and the co-ordinates of

\mathrm{A}

are

(3,-6,10)

then the co-ordinates of

\mathrm{B}

are
A line

A B

in three-dimensional space makes angles

45^{\circ}

and

120^{\circ}

with the positive

X

-axis and the positive

Y

-axis, respectively. If

A B

makes an acute angle

\theta

with the positive

Z

-axis, then

\theta

equals