JEE MATHEMATICS MCQ: DCS AND DRS

1 Easy

1 of 1

Analyzing +4 | -1

The vector equations of two lines

L_1

and

L_2

are respectively

r = 17i - 9j + 9k + \lambda (3i + j + 5k)

and

r = 15i - 8j - k + \mu (4i + 3j)

L_1

and

L_2

are skew lines.

II.

(11,-11,-1)

is the point of intersection of

L_1

and

L_2

.

III.

(-11,11,1)

is the point of intersection of

L_1

and

L_2

.

IV.

\cos ^{-1}\left(\frac{3}{\sqrt{35}}\right)

is the acute angle between,

L_1

and

L_2

.

Then, which of the following is true?

View answer and explanation

Correct option: B

I and IV

Option B (I and IV) is correct because lines L1 and L2 are skew lines, and the acute angle between them is calculated as cos^-1(3/sqrt(35)).

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