The distance of the point having position vector - hati + 2 hatj + 6 hatk from the straight line passing through the point (2, 3, -4) and parallel to the vector, 6 hati + 3 hatj - 4 hatk is :

Question

The distance of the point having position vector - hati + 2 hatj + 6 hatk from the straight line passing through the point (2, 3, -4) and parallel to the vector, 6 hati + 3 hatj - 4 hatk is : (A) 7 (B)  4 √3 (C)  2 √ 13 (D) 6

Tardigrade Admin · Accepted Answer

AD = |(AP . vecn/| vecn|)| = √61 ⇒ PD = √AP2 -AD2 = √110-61 = 7

Q. The distance of the point having position vector $- \hat{i} + 2 \hat{j} + 6 \hat{k}$ from the straight line passing through the point $(2, 3, - 4)$ and parallel to the vector, $6 \hat{i} + 3 \hat{j} - 4 \hat{k}$ is :

$7$

$43$

$213$

$6$

$A D = ∣ ∣ \frac{A P . n}{∣ n ∣} ∣ ∣ = 61$
$\Rightarrow P D = A P^{2} - A D^{2} = 110 - 61 = 7$

Q. The distance of the point having position vector −i^+2j^​+6k^ from the straight line passing through the point (2,3,−4) and parallel to the vector, 6i^+3j^​−4k^ is :

7

43​

213​

6

AD=∣∣​∣n∣AP.n​∣∣​=61​ ⇒PD=AP2−AD2​=110−61​=7

Q. The distance of the point having position vector $- \hat{i} + 2 \hat{j} + 6 \hat{k}$ from the straight line passing through the point $(2, 3, - 4)$ and parallel to the vector, $6 \hat{i} + 3 \hat{j} - 4 \hat{k}$ is :

$7$

$43$

$213$

$6$

$A D = ∣ ∣ \frac{A P . n}{∣ n ∣} ∣ ∣ = 61$
$\Rightarrow P D = A P^{2} - A D^{2} = 110 - 61 = 7$