Q. 64.0( 4 Votes )

# <span lang="EN-US

Answer :

Given: and is equally inclined with an acute with the coordinate axes

To find: the vector and Cartesian forms of the equation of a plane which passes through (2, 1, -1) and is normal to Let has direction cosines as l, m and n and it makes an angle of α, β and γ with the coordinate axes. So as per the given condition

α=β=γ

cos α =cos β =cos γ

l=m=n=p (let assume)

We know that,

l2+m2+n2=1

p2+p2+p2=1

3p2=1 So,  For the negative value of cos the angles are obtuse so that we will neglect it

So we have Hence So the vector equation of the normal becomes,   The plane is passing through the point (2, 1, -1). Let the position vector of this point be We know that vector equation of a plane passing through point and perpendicular/normal to the vector is given by Substituting the values from eqn(i) and eqn(ii) in the above equation, we get   (by multiplying the two vectors using the formula )  is the vector and Cartesian forms of the equation of a plane which passes through (2, 1, -1) and is normal to .

Let Then, the above vector equation of the plane becomes, Now multiplying the two vectors using the formula , we get  This is the Cartesian form of the equation of a plane which passes through (2, 1, -1) and is normal to .

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Find the angle beMathematics - Board Papers

If two vectors <sMathematics - Board Papers

If <span lang="ENMathematics - Exemplar

Show that area ofMathematics - Exemplar

Find the equationMathematics - Board Papers

Using vectors, fiMathematics - Board Papers

Find the angle beMathematics - Board Papers

Find the positionMathematics - Board Papers

<span lang="EN-USMathematics - Board Papers

If vectors <span Mathematics - Board Papers