# Find the value of k so that the lines and are perpendicular

Asked on by bethhgz

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to write the parametric equations of the lines `d_1`  and `d_2`  such that:

`x_1 = 3 + (3k+1)*t`

`y_1 = -6 + 2t`

`z_1 = -3 + 2k*t`

`x_2 = -7 + 3s`

`y_2 = -8 - 2ks`

`z_2 = -9 - 3s`

You need to write the vector lines such that:

`bar d_1 = lt3,-6,-3gt + t*lt(3k+1,2,2k)gt`

`bar d_2 = lt-7,-8,-9gt + s*lt3,-2k,-3gt`

The lines `d_1`  and `d_2`  are perpendicular if the dot product `bar d_1*bar d_2 = 0`  such that:

`lt(3k+1,2,2k)gt*lt3,-2k,-3gt = 0`

`3k + 1 = 3=gt k_1 = 2/3`

`-2k=2 =gt k_2 = -1`

`2k=-3 =gt k_3 = -3/2`

Hence, evaluating the values of k for the lines are perpendicular yields `k_1 = 2/3,k_2 = -1,k_3 = -3/2.`

bethhgz | Student, Undergraduate | (Level 1) eNoter

Posted on

and

x-3 / 3k+1 = y+6/2= z+3/2k

and x+7/3 = y+8/-2k = x+9/-3

SOrry those are the equations. Forgot to put them up

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