Question

Plane 2x+3y+6z-15=0 makes angle of measure ....... with X-axis.Select the correct option from the given options.
(a) cos⁻¹ 3√5/7
(b) sin⁻¹ 3/7
(c) sin⁻¹ 2/√7
(d) tan⁻¹ 2/7

Answer 1

for solution refer attachment and ur answer is option a

Answer 2

angle made by plane ax + by + cz + d = 0 with X axis is $sin^{-1}\frac{a}{\sqrt{a^2+b^2+c^2}}$ , with Y -axis is $sin^{-1}\frac{b}{\sqrt{a^2+b^2+c^2}}$ and with Z - axis is $sin^{-1}\frac{c}{\sqrt{a^2+b^2+c^2}}$

here, equation of plane is 2x + 3y + 6z -15 = 0
hence, a = 2 , b = 3 and c = 6

so, angle made with X - axis is $sin^{-1}\frac{2}{\sqrt{2^2+3^2+6^2}}$

=$sin^{-1}\frac{2}{\sqrt{4+9+36}}$

=$sin^{-1}\frac{2}{7}$

so, $cos^{-1}\sqrt{1-\frac{2^2}{7^2}}$

=$cos^{-1}\sqrt{\frac{49-4}{49}}$

=$cos^{-1}\frac{3\sqrt{5}}{7}$

hence, option (a) is correct.