Question

(iv) If the line r = (– 2 j + 3k) +a (2î + i + 2k) is parallel to
the plane r:(3-2 +mk)=10, then value of m is​

Answer 1

Answer:

The value of m is - 2  for the given vectors

Step-by-step explanation:

Given as :

The line r = ( - 2 j + 3 k ) + a ( 2 i + j + 2 k)

The plane = r . ( 3 i - 2 j + m k ) = 10

According to question

b = ( 2 i + j + 2 k )

n =  ( 3 i - 2 j + m k )

The line is parallel to the plane

So, b. n = 0

i.e  ( 2 i + j + 2 k )  .   ( 3 i - 2 j + m k )  = 0

Or, ( 2 i . 3 i ) - ( 2 i . 2 j ) + ( 2 i . m k ) - ( j . 2 j ) + ( j . m k ) + ( 2 k . 3 i ) - ( 2 k . 2 j) + ( 2 k . m k ) = 0

Or, 6 - 0 + 0 - 2 + 0 + 0 - 0 + 2 m = 0          ( ∵  i . i = j . j = k . k = 1 )

Or, 4 + 2 m = 0

Or, 2 m = - 4

∴     m = $\dfrac{-4}{2}$

i.e m = - 2

Hence, The value of m is - 2  for the given vectors Answer