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Murtaza Nimachwala

Dec 10, 2014

#### Find the angle between the lines whose direction cosines are given by the equations 3l + m + 5n = 0 and 6mn - 2nl + 5lm = 0



Sol:
Given lines are 3l + m + 5n = 0

m = - (3l + 5n) -----------(1)

and 6mn - 2nl + 5lm = 0 ----------(2)

Substitute m in equation (2) we obtain
...

Anubhav Singh

Feb 9, 2015

#### what are the direction ratios of a line equally inclined to the axes? How many such lines are there ? please explain all the necessary steps in detail along with the formulas used and the diagram ?



If a line makes angles α,β,ɣ with the axes we have α = β = ɣ .
cos α = cos β = cos ɣ or l = m = n .
l2 + m2 + n2 = 1
l2 + l2...

Haris Sherwani

Jan 14, 2015

#### 1) Reduce the equation of the plane 3x - 4y + z = 9 to the intercept form and hence find the intercepts made by the plane with the coordinate axes. 2) Write the equation of the plane whose intercepts on the coordinate axes are 2,-4,5 respectively.



Sol:1)
Equation of the plane 3x - 4y + z = 9  [ dividing 9 on both sides ]

⇒ (3x / 9) + (-4y / 9) +( z / 9) = 1

⇒ (x / 3) + (y / (-9 / 4)) +( z / 9) = 1

Shakti Gayatri

Jan 20, 2015

#### The statement is true or false , answer with explaination If two lines are perpendicular to a third line , then the direction ratios of the two lines are proportional.



True.

The direction ratios are proportional only if the two lines are on the same plane otherwise they are not proportional.

Shakti Gayatri

Feb 9, 2015

#### Find the vector and cartesian equations of the planes, that passes through the point (1,4,0) and the normal vector to the plane is i-2j+k



Given cartesian equations of the plane, that passes through the point (1,4,0) .

a = i + 4j and normal to the vector n = i - 2j + k

we know that cartesian equations of the plane tha...

Shakti Gayatri

Jan 20, 2015

#### If l,m,n be three real numbers proportional to the direction cosines of a line L.then l²+m²+n²=1. (answer if the statement is true or false with explaination)



M N Ramdas M.N.Ramdas

Jan 12, 2015

#### Find the equation of circle passing through (0, 0) and having the radius 4 units and whose center is lying on the line 2x + 3y -12 = 0.



Pl use the link below to find the solution:

Harsh Aryan

May 26, 2015

#### show that the line through the point(4,7,8) and (2,3,4) is parallel to the line through the point (-1,-2,1) and (1,2,5)



drs are in propotion

Shakti Gayatri

Jan 25, 2015

#### Prove the measure of the angle between the diagonal of a and the diagonal of a cube , drawn from a vertex is cos^-1√2/√3



Your question is incorrect.Please recheck and repost the question with proper data.

Murtaza Nimachwala

Dec 10, 2014

#### Find the angle between the lines whose direction cosines are given by the equations 3l + m + 5n = 0 and 6mn - 2nl + 5lm = 0



Sol:
Given lines are 3l + m + 5n = 0

m = - (3l + 5n) -----------(1)

and 6mn - 2nl + 5lm = 0 ----------(2)

Substitute m in equation (2) we obtain
...

Anubhav Singh

Feb 9, 2015

#### what are the direction ratios of a line equally inclined to the axes? How many such lines are there ? please explain all the necessary steps in detail along with the formulas used and the diagram ?



If a line makes angles α,β,ɣ with the axes we have α = β = ɣ .
cos α = cos β = cos ɣ or l = m = n .
l2 + m2 + n2 = 1
l2 + l2...

Haris Sherwani

Jan 14, 2015

#### 1) Reduce the equation of the plane 3x - 4y + z = 9 to the intercept form and hence find the intercepts made by the plane with the coordinate axes. 2) Write the equation of the plane whose intercepts on the coordinate axes are 2,-4,5 respectively.



Sol:1)
Equation of the plane 3x - 4y + z = 9  [ dividing 9 on both sides ]

⇒ (3x / 9) + (-4y / 9) +( z / 9) = 1

⇒ (x / 3) + (y / (-9 / 4)) +( z / 9) = 1

Shakti Gayatri

Jan 20, 2015

#### The statement is true or false , answer with explaination If two lines are perpendicular to a third line , then the direction ratios of the two lines are proportional.



True.

The direction ratios are proportional only if the two lines are on the same plane otherwise they are not proportional.

Shakti Gayatri

Feb 9, 2015

#### Find the vector and cartesian equations of the planes, that passes through the point (1,4,0) and the normal vector to the plane is i-2j+k



Given cartesian equations of the plane, that passes through the point (1,4,0) .

a = i + 4j and normal to the vector n = i - 2j + k

we know that cartesian equations of the plane tha...

Shakti Gayatri

Jan 20, 2015

#### If l,m,n be three real numbers proportional to the direction cosines of a line L.then l²+m²+n²=1. (answer if the statement is true or false with explaination)



M N Ramdas M.N.Ramdas

Jan 12, 2015

#### Find the equation of circle passing through (0, 0) and having the radius 4 units and whose center is lying on the line 2x + 3y -12 = 0.



Pl use the link below to find the solution:

Harsh Aryan

May 26, 2015

#### show that the line through the point(4,7,8) and (2,3,4) is parallel to the line through the point (-1,-2,1) and (1,2,5)



drs are in propotion

Shakti Gayatri

Jan 25, 2015

#### Prove the measure of the angle between the diagonal of a and the diagonal of a cube , drawn from a vertex is cos^-1√2/√3



Your question is incorrect.Please recheck and repost the question with proper data.

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