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Maths NCERT Exemplar Solutions Class 12th Chapter Three Determinants Ncert Solutions Maths class 12th Maths Class 12th

Let the plane ax + by + cz = d pass through (2, 3, -5) and its perpendicular to the planes

2x + y – 5z = 10 and 3x + 5y – 7z = 12.

If a, b, c, d are integers d > 0 and then the value of a + 7b + c + 20d is equal to:

Option 1 -

Option 2 -

Option 3 -

Option 4 -

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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 4

Detailed Solution:

ax + by + cz = d

2a + 3b – 5c = d 2a + 3b – 5c = d …………….(v)

Putting (i) & (iv) in (v) we get a = -9d.

In conditions

$(2 \hat{i} + \hat{j} - 5 \hat{k}), (a \hat{i} + b \hat{j} + c \hat{k}) = 0$

2b = d ………….(i) d > 0

2a + b – 5c = 0 2a + 3b – 5c = d $| a |, | b |, | c |, d \to g . c . d$

= $\frac{α}{2}$

$∴ \frac{α}{2} = 1 \Rightarrow α = 2$

$(3 \hat{i} + 5 \hat{j} - 7 \hat{k}) . (a \hat{i} + b \hat{j} + c \hat{k}) = 0$

3a + 5b – 7c = 0) × $\frac{4}{7} . . . . . . . . . . . . . . . . . . . (i i i)$

$∴ a = - 18, b = 1$

c = -7, d = 2

(iii)…(ii) ® 2a + 3b $\frac{- 33 c}{7} = 0$

2a + 3b = $\frac{33}{7} c$ $c = \frac{- 7}{2} d . . . . . . . . . . . . . . . . . (i v)$

...more

ax + by + cz = d

2a + 3b – 5c = d 2a + 3b – 5c = d …………….(v)

Putting (i) & (iv) in (v) we get a = -9d.

In conditions

$(2 \hat{i} + \hat{j} - 5 \hat{k}), (a \hat{i} + b \hat{j} + c \hat{k}) = 0$

2b = d ………….(i) d > 0

2a + b – 5c = 0 2a + 3b – 5c = d $| a |, | b |, | c |, d \to g . c . d$

= $\frac{α}{2}$

$∴ \frac{α}{2} = 1 \Rightarrow α = 2$

$(3 \hat{i} + 5 \hat{j} - 7 \hat{k}) . (a \hat{i} + b \hat{j} + c \hat{k}) = 0$

3a + 5b – 7c = 0) × $\frac{4}{7} . . . . . . . . . . . . . . . . . . . (i i i)$

$∴ a = - 18, b = 1$

c = -7, d = 2

(iii)…(ii) ® 2a + 3b $\frac{- 33 c}{7} = 0$

2a + 3b = $\frac{33}{7} c$ $c = \frac{- 7}{2} d . . . . . . . . . . . . . . . . . (i v)$

Putting values

a + 7b + c + 20d = 22

less

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Let the plane ax + by + cz = d pass through (2, 3, -5) and its perpendicular to the planes

2x + y – 5z = 10 and 3x + 5y – 7z = 12.

If a, b, c, d are integers d > 0 and then the value of a + 7b + c + 20d is equal to:

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Let the plane ax + by + cz = d pass through (2, 3, -5) and its perpendicular to the planes 2x + y – 5z = 10 and 3x + 5y – 7z = 12. If a, b, c, d are integers d > 0 and then the value of a + 7b + c + 20d is equal to:

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Let the plane ax + by + cz = d pass through (2, 3, -5) and its perpendicular to the planes

2x + y – 5z = 10 and 3x + 5y – 7z = 12.

If a, b, c, d are integers d > 0 and then the value of a + 7b + c + 20d is equal to: