Let A be a point on the line and B = (3,2,6) be a point in the space. Then the value of for which the vector is parallel to plane is:

Question

Let A be a point on the line $\vec{r} = (1 - 3 μ) \hat{i} + (μ - 1) \hat{j} + (2 + 5 μ) \hat{k}$ and B = (3,2,6) be a point in the space. Then the value of $' 4 μ'$ for which the vector $\bar{A B}$ is parallel to plane $x - 4 y + 3 z = 1$ is:

Smart Achievers · Accepted Answer

(1)

$Let A is (1 - 3 μ, μ - 1, 2 + 5 μ)$

$\bar{A B} = (3 μ + 2) \hat{i} + (3 - μ) \hat{j} + (4 - 5 μ) \hat{k} which is parallel to plane x - 4 y + 3 z = 1$

$- 8 μ + 2 = 0 \Rightarrow μ = \frac{1}{4}$ $∴$ $4 μ = 1$

Solution

Q.
Let A be a point on the line $\vec{r} = (1 - 3 μ) \hat{i} + (μ - 1) \hat{j} + (2 + 5 μ) \hat{k}$ and B = (3,2,6) be a point in the space. Then the value of $' 4 μ'$ for which the vector $\bar{A B}$ is parallel to plane $x - 4 y + 3 z = 1$ is:

1 $1$

2 $\frac{1}{8}$

3 $\frac{1}{2}$

4 $- 1$

Ans.
(1)

$Let A is (1 - 3 μ, μ - 1, 2 + 5 μ)$

$\bar{A B} = (3 μ + 2) \hat{i} + (3 - μ) \hat{j} + (4 - 5 μ) \hat{k} which is parallel to plane x - 4 y + 3 z = 1$

$- 8 μ + 2 = 0 \Rightarrow μ = \frac{1}{4}$ $∴$ $4 μ = 1$

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Solution

Q. Let A be a point on the line r→=(1-3μ)i^+(μ-1)j^+(2+5μ)k^ and B = (3,2,6) be a point in the space. Then the value of '4μ' for which the vector AB¯ is parallel to plane x-4y+3z=1 is:

1 1

2 18

3 12

4 -1

Ans. (1) Let A is (1-3μ,μ-1,2+5μ) AB¯=(3μ+2)i^+(3-μ)j^+(4-5μ)k^ which is parallel to plane x-4y+3z=1 -8μ+2=0⇒μ=14 ∴ 4μ=1