Question

If the lines 3x-4y+7 =0 and 2x +ky +5=0 are perpendicular to each other, then the value of k is, *
3/2
-3/2
2/3
-2/3
​

Answer 1

Step-by-step explanation:

Given, lines 3x-4y+7 =0 and 2x +ky +5=0 are perpendicular to each other

=> product of their slopes = -1

=> ( -3/-4 ) ( -2/k ) = -1

=> k = -4 / 6 = -2 /3

Answer 2

The value of k is 3/2.

Option (1) is correct.

Given:

• $3x - 4y + 7 = 0 \: and \: 2x + ky + 5 = 0$
• Two lines are perpendicular to each other.

To find:

• Find the value of k.

1. 3/2
2. -3/2
3. 2/3
4. -2/3

Solution:

Concept to be used:

• Slope intercept form of straight line is $\bf y = mx + c$, where m is slope of line.
• If two lines are perpendicular and their slopes are m1 and m2, then $\bf m_1m_2=-1$

Step 1:

Find the slope of both lines.

Convert the line of equation in slope-intercept form.

$3x - 4y + 7 = 0$

or

$- 4y = - 3x - 7$

or

$\bf y = \frac{3}{4} x + \frac{7}{4}$

let the slope of this line is m1.

$\bf m_1 = \frac{3}{4}$

by the same way, slope of second line is

$\bf m_2 = - \frac{2}{k}$

Step 2:

Apply the condition of perpendicularity.

$\frac{3}{4} \times \left ( \frac{ - 2}{k}\right )= - 1$

or

$- \frac{3}{2k} = - 1$

or

$k = \frac{3}{2}$

Thus,

Value of k is 3/2.

Option (1) is correct.

____________________________

Learn more:

1) If the graph of 2x+3y − 6=0 is perpendicular to the graph of ax − 3y=5. What is the value of a?

https://brainly.in/question/12649748

2) Find the value of 'k' for which the pair of equations 2x - ky + 3 = 0, 4x + 6y - 5 =0 represent parallel lines.

https://brainly.in/question/5483702