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131. Determine whether the following pair of lines intersect:

fraction numerator straight x minus 1 over denominator 2 end fraction space equals fraction numerator straight y plus 1 over denominator 3 end fraction space equals straight z

fraction numerator straight x plus 5 over denominator 5 end fraction space equals space fraction numerator straight y minus 2 over denominator 1 end fraction comma space space straight z space equals space 2

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132. Find the intercepts cut off by the plane x + 2y – 2z = 9 with the axes.

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133. Find the equation of the plane with intercepts 2, 3 and 4 on the x, y and z-axis respectively.

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134. Find the intercepts cut off by the plane 2x + y – z = 5.

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135. Find the intercept form of the equation of the plane x + 3 y – 7 z + 2 = 0.

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136. Find the equation of the plane with intercept 3 on the y-axis and parallel to ZOX plane..

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The equation of plane is x + 2y’ + 3z – 6 = 0
Direction-ratios of a normal to the plane are 1, 2, 3.
Dividing each by

square root of left parenthesis 1 right parenthesis squared plus left parenthesis 2 right parenthesis squared plus left parenthesis 3 right parenthesis squared end root space equals space square root of 14 comma

the direction-cosines of a normal to the given plane are

fraction numerator 1 over denominator square root of 14 end fraction comma space fraction numerator 2 over denominator square root of 14 end fraction comma space fraction numerator 3 over denominator square root of 14 end fraction

∴ the normal vector to the given plabne is

fraction numerator 1 over denominator square root of 14 end fraction straight i with hat on top plus space fraction numerator 2 over denominator square root of 14 end fraction straight j with hat on top space plus space fraction numerator 3 over denominator square root of 14 end fraction straight k with hat on top.

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138. Find the normal form of the equation of the plane 3x– 4y + z + 5 = 0.

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139. Find the value of k for which the planes 3 x– 6 y– 2 z = 7 and 2x + y'– k z = 5 are perpendicular to each other.

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140.

The foot of the perpendicular drawn from the origin to the plane is (4, 3, 2). Find the equation of the plane.

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