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If 7x + 6y - 2z = 0, 3x + 4y + 2z = 0, x...

If `7x + 6y - 2z = 0, 3x + 4y + 2z = 0, x - 2y - 6z = 0` then which option is correct

A

infinitely many solutions, (x,y,z) satisfying y = 2z.

B

infinitely many solutions, (x,y,z) satisfying x = 2z.

C

no solution

D

only the trivial solution.

Text Solution

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The correct Answer is:
B
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2x + 3y-5z = 7, x + y + z = 6,3x-4y + 2z = 1, then x =

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Add 2x - 3y + z , 5y - x + 7z and 3x - y - 6z.

23. The system of equations 4x+6y + 8z= 0 7x + 8y + 9z = 0 3x + 2y+ z = 0 has (a) no solution (b) only one solution (c) two solutions (d) infinite number of solutions

If x =a, y=b, z=c is a solution of the system of linear equations x + 8y + 7z =0, 9 x + 2y + 3z =0, x + y+z=0 such that point (a,b,c ) lies on the plane x + 2y + z=6, then 2a+ b+c equals

lambda x + 2y + 2z = 5, 2lambda x + 3y + 5z = 8, 4x + lambda y + 6z = 10 for the system of equation check the correct option.

In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them : (a) 7x + 5y + 6z + 30 = 0 and 3x - y - 10 z + 4 = 0 (b) 2x + y + 3z -2 = 0 and x - 2y + 5 = 0 (c) 2x - 2y + 4z + 5 = 0 and 3x - 3y + 6z - 1 = 0 (d) 2x - y + 4z + 5 = 0 and 2x - y + 3z + 3 = 0 (e) 4 x + 8y + z = 0 and y + z - 4 = 0

In the following determine whether the given planes are parallel or perpendicular and in case they are neither, find the angles between them : (i) 7x + 5y + 6z + 30 = 0 and 3x - y - 10z + 4 = 0 (ii) 2x + y + 3z - 2 = 0 and x - 2y + 5 = 0 (iii) 2x - 2y + 4z + 5 = 0 and 3x - 3y + 6z - 1 = 0 (iv) 2x - y + 3z - 1 = 0 and 2x - y + 3z + 3 = 0 (v) 4x + 8y + z - 8 = 0 and y + z - 4 = 0.

Find the angle between the planes : (i) 3 x - 6y - 2z = 7 " " 2x + y - 2z = 5 (ii) 4 x + 8y + z = 8 " " and y + z = 4 (iii) 2 x - y + z =6 " " and x + y + 2z = 7 .

Add: 5x - 8y + 2z, 3z - 4y - 2x, 6y - z - x and 3x - 2z - 3y

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