Question

If the vectors = $\left( \tan \alpha , - 1,2 \sqrt { \tan \frac { \alpha } { 2 } } \right)$,

= $\left( \tan \alpha , \tan \alpha , \frac { - 3 } { \sqrt { \sin \frac { \alpha } { 2 } } } \right)$ are orthogonal and vector

= (1, 3, sin 2a) makes an obtuse angle with z- axis then a equals:

• A. (2n +1)p + tan^–1 2
• B. (2n + 1)p– tan^–12
• C. np – tan^–1 2
• D. None of these

Answer 1

Answer: (B)

(2n + 1)p– tan^–12

Answer 2

$\overrightarrow { \mathrm { b } }$ perpendicular $\overrightarrow { \mathrm { c } }$ ̃ $\overrightarrow { \mathrm { b } }$ . $\overrightarrow { \mathrm { c } }$ = 0

̃ tan² a – tan a – 6 = 0 ̃ tan a = 3, –2 also make an obtuse angle with z- axis therefore . < 0 ̃ sin 2a < 0

if tan a = 3 then sin 2a = $\frac { 2 \tan \alpha } { 1 + \tan ^ { 2 } \alpha }$= $\frac { 4 } { 3 }$> 0 Now tan 2a > 0, sin 2a < 0 ̃ a Î third quadrant and tan a = –2

̃ tan (p – a) = 2 ̃ a = (2n +1) p – tan^–1 2, n Î I