If the plane 2x - 3y + 6z - 11 = 0 makes an angle - 1 with X -axis, then the value of is

Since, 2x - 3y + 6z - 11 = 0 makes an angle - 1 with X-axis. = (1 + 0 + 0 ) and = 2 - 3 + 6 As we know, = | | | | | = ) (2 - 3 + 6 )| 1 = 7

Three Dimensional Geometry — Class 12 Maths Solution

exemplar objective MCQ NCERT,Exemp.Q.36,Page.238

Question

If the plane $2x - 3y + 6z - 11 = 0$ makes an angle ${\sin ^{ - 1}}\alpha$ with $X$-axis, then the value of $\alpha$ is

(a) $\frac{{\sqrt 3 }}{2}$
(b) $\frac{{\sqrt 2 }}{3}$
(c) $\frac{2}{7}$ ✓ Correct
(d) $\frac{3}{7}$

Step-by-step Solution

Since, $2x - 3y + 6z - 11 = 0$ makes an angle ${\sin ^{ - 1}}\alpha$ with X-axis.

$\overrightarrow {\rm{b}} = (1\widehat {\rm{i}} + 0\widehat {\rm{j}} + 0\widehat {\rm{k}})$

and $\overrightarrow {\rm{n}} = 2\widehat {\rm{i}} - 3\widehat {\rm{j}} + 6\widehat {\rm{k}}$

As we know, $\sin \theta = \frac{{|\overrightarrow {\rm{b}} \cdot \overrightarrow {\rm{n}} |}}{{|\overrightarrow {\rm{b}} | \cdot |\overrightarrow {\rm{n}} |}}$

$= \frac{{|(1\widehat {\rm{i}}) \cdot (2\widehat {\rm{i}} - 3\widehat {\rm{j}} + 6\widehat {\rm{k}})|}}{{\sqrt 1 \sqrt {4 + 9 + 36} }} = \frac{2}{7}$

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