Question

Find a vector v, parallel to the intersection of the planes 2x+3y+6z=4 and 2x-2y-2z=-7​

Answer 1

Answer:

Given :-

Ratio of length breadth and height = 1:2:3

TSA = 792 sq. m

To Find :-

Volume

Solution :-

Let,

Length = x

breadth = 2x

Height = 3x

\bf\red{TSA = 2(lb + bh +lh)}TSA=2(lb+bh+lh)

\sf 792 = 2(x\times 2x +2 x\times 3x+ x\times 3x)792=2(x×2x+2x×3x+x×3x)

\sf 792=2(2x^{2} +6x^{2} +3x^{2} )792=2(2x

2

+6x

2

+3x

2

)

\sf 792 = 2(11x^{2} )792=2(11x

2

)

\sf\dfrac{792}{2} = 11x^2

2

792

=11x

2

\sf 396 = 11x^{2}396=11x

2

\sf \dfrac{396}{11} = x^{2}

11

396

=x

2

\sf 36 = x^{2}36=x

2

\sf \sqrt{36} =\sqrt{x^2}

36

=

x

2

\sf 6 = x6=x

Length = 6 m

Breadth = 2(6) = 12 m

Height = 3(6) = 18 m

~Finding volume

\bf Volume = l\times b \times hVolume=l×b×h

\sf Volume = 6 \times12\times18Volume=6×12×18

\sf Volume = 1296 m^{3}Volume=1296m

3