The direction ratios of two lines L1 and L2 are and respectively- A vector V is perpendicular to L1 and L2 both such that -V-15- If V-x1-x2-x3k- then the value of -x1-x2-x3- is

Vector perpendicular to L_1 and L_2 is nbsp; î amp; ĵ amp; k̂ nbsp; 4 amp; 1 amp; 3 nbsp; 2 amp; 1 amp; 2 =î( 2+3) ĵ(8 6)+k̂( 4+2) =î ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Condition for a Line to Lie on a Plane

The direction...

Question

The direction ratios of two lines $L_{1}$ and $L_{2}$ are $< 4, - 1, 3 >$ and $< 2, - 1, 2 >$ respectively. A vector $\to V$ is perpendicular to $L_{1}$ and $L_{2}$ both such that $| \to V | = 15$ . If $\to V = x_{1}^i + x_{2}^j + x_{3}^k,$ then the value of $| x_{1} + x_{2} + x_{3} |$ is

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

15.00

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

15.0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

Vector perpendicular to $L_{1}$ and $L_{2}$ is
$∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 4 & - 1 & 3 2 & - 1 & 2 \end{matrix} ∣ ∣ ∣ ∣ ∣$
$=^i (- 2 + 3) -^j (8 - 6) +^k (- 4 + 2)$
$=^i - 2^j - 2^k$

Given, $\to V = λ (^i - 2^j - 2^k)$
Also, $| - - \to P Q | = 15$
$\Rightarrow λ^{2} (1 + 4 + 4) = (15)^{2}$
$\Rightarrow λ = \pm 5$
$∴ - - \to P Q = \pm (5^i - 10^j - 10^k)$
Hence, the value of $| x_{1} + x_{2} + x_{3} |$ is $15.$

Suggest Corrections

Similar questions

Q. Let

L_{1}

and

L_{2}

be the lines whose equation are

\frac{x - 3}{3} = \frac{y - 8}{- 1} = \frac{z - 3}{1}

and

\frac{x + 3}{- 3} = \frac{y + 7}{2} = \frac{z - 6}{4}

respectively A and B are two points on

L_{1}

and

L_{2}

respectively such that AB is perpendicular both the lines

L_{1}

and

L_{2}

.Find points A, B and hence find shortest distance between lines

L_{1}

and

L_{2}

Q. If points (h, k)

(1, 2)

and

(- 3, 4)

lie on line

L_{1}

and points (h, k) and

(4, 3)

lie on

L_{2}

. If

L_{2}

is perpendicular to

L_{1}

, then value of

\frac{h}{k}

is?

Q. Direction ratio of two lines are

l_{1}, m_{1}, n_{1}

and

l_{2}, m_{2}, n_{2}

then direction ratios of the line perpendicular to both the lines are

Q. Consider the following statements relating to 3 lines

L_{1}

L_{2}

and

L_{3}

in the same plane
(1). If

L_{2}

and

L_{3}

are both parallel to

L_{1}

, then they are parallel to each other.
(2). If

L_{2}

and

L_{3}

are both perpendicular to

L_{1}

, then they are parallel to each other.
(3). If the acute angle between

L_{1}

and

L_{2}

is equal to to acute angle between

L_{1}

and

L_{3}

, then

L_{2}

is parallel to

L_{3}

Of these statements:

Q. let

P

and

Q

are any two points on the circle

x^{2} + y^{2} = 4

such that

P Q

is a diameter. If

L_{1}

and

L_{2}

are the lengths of perpendicular from

P

and

Q

x + y = 1

, then the maximum value of

L_{1}, L_{2}

Join BYJU'S Learning Program

The direction ratios of two lines L1 and L2 are <4,−1,3> and <2,−1,2> respectively. A vector →V is perpendicular to L1 and L2 both such that |→V|=15. If →V=x1^i+x2^j+x3^k, then the value of |x1+x2+x3| is

Vector perpendicular to L1 and L2 is ∣∣ ∣ ∣∣^i^j^k4−132−12∣∣ ∣ ∣∣ =^i(−2+3)−^j(8−6)+^k(−4+2) =^i−2^j−2^k Given, →V=λ(^i−2^j−2^k) Also, |−−→PQ|=15 ⇒λ2(1+4+4)=(15)2 ⇒λ=±5 ∴−−→PQ=±(5^i−10^j−10^k) Hence, the value of |x1+x2+x3| is 15.

The direction ratios of two lines $L_{1}$ and $L_{2}$ are $< 4, - 1, 3 >$ and $< 2, - 1, 2 >$ respectively. A vector $\to V$ is perpendicular to $L_{1}$ and $L_{2}$ both such that $| \to V | = 15$ . If $\to V = x_{1}^i + x_{2}^j + x_{3}^k,$ then the value of $| x_{1} + x_{2} + x_{3} |$ is