MHT CET 2023 9th May Morning Shift | Three Dimensional Geometry Question 54 | Mathematics

$$\overline{\mathrm{r}}=\left(\frac{1}{3} \hat{\mathrm{i}}-\frac{1}{3} \hat{\mathrm{j}}+\hat{\mathrm{k}}\right)+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$

$$\overline{\mathrm{r}}=(\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$

$$\overline{\mathrm{r}}=\left(\frac{-1}{3} \hat{\mathrm{i}}+\frac{1}{3} \hat{\mathrm{j}}+\hat{\mathrm{k}}\right)+\lambda(\hat{\mathrm{i}}-2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}})$$

$$\overline{\mathrm{r}}=\left(\frac{1}{3} \hat{\mathrm{i}}-\frac{1}{3} \hat{\mathrm{j}}-\hat{\mathrm{k}}\right)+\lambda(\hat{\mathrm{i}}-\hat{\mathrm{j}}+\hat{\mathrm{k}})$$

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

The distance between parallel lines

$$\frac{x-1}{2}=\frac{y-2}{-2}=\frac{z-3}{1}$$ and

$$\frac{x}{2}=\frac{y}{-2}=\frac{z}{1}$$ is :

$$\frac{2 \sqrt{5}}{3}$$ units

$$\frac{\sqrt{5}}{3}$$ units

$$\frac{5 \sqrt{5}}{3}$$ units

$$\frac{4 \sqrt{5}}{3}$$ units

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

A line makes the same angle '$$\alpha$$' with each of the $$x$$ and $$y$$ axes. If the angle '$$\theta$$', which it makes with the $$z$$-axis, is such that $$\sin ^2 \theta=2 \sin ^2 \alpha$$, then the angle $$\alpha$$ is

$$\left(\frac{\pi}{4}\right)$$

$$\left(\frac{\pi}{2}\right)$$

$$\left(\frac{\pi}{3}\right)$$

$$\left(\frac{\pi}{6}\right)$$

MHT CET 2022 11th August Evening Shift

MCQ (Single Correct Answer)

-0

A tetrahedron has verticles $$P(1,2,1), Q(2,1,3), R(-1,1,2)$$ and $$O(0,0,0)$$. Then the angle between the faces $$O P Q$$ and $$P Q R$$ is

$$\cos ^{-1}\left(\frac{17}{35}\right)$$

$$\cos ^{-1}\left(\frac{17}{31}\right)$$

$$\cos ^{-1}\left(\frac{19}{35}\right)$$

$$\cos ^{-1}\left(\frac{19}{31}\right)$$

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