Question

(i) Find the value of k, if the perpendicular distance of the plane 2x + 3y – z = k from the
origin is √14
​

Answer 1

Step-by-step explanation:

d=| Ax+By+Cz-D| / square root of A^2+B^2+C^2

A=2,B=3,C=-1 ,D=k ,d =square root of 14 ; At(0,0,0) ; square root of 14=|k| / square root of 14 ; k=14

Answer 2

The value of 'k' is 14

Given:

The perpendicular distance of the plane 2x + 3y - z = k from origin is √14  

To find:

The value of k

Solution:

Formula used:

The formula perpendicular distance of the plane to a point (x, y, z) is  

          d = |(ax + by + cz + d) / √(a² + b² + c²)|

From the given data,

The equation of the plane is 2x + 3y – z = k  

=> a = 2, b = 3, c = -1 and d = - k

The coordinates of the origin are (0, 0, 0)  

=> x = 0, y = 0, and z = 0

Using the above formula,

=> d =  |(2(0) + 3(0) + (-1)(0) + k) / √(2² + 3² + (-1)²)|  

=> d = | k / √ 4 + 9 + 1|    

=> d = k/√14

From the given data the distance is √14

=> √14 = k/√14  

=> k = (√14)(√14)

=> k = 14  

Therefore,

The value of 'k' is 14

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