Question

Help me with this.
The angle between \[3i-j\] and \[2i+\lambda j\] is \[\frac{pi}{4}\]. Find the value of \[\lambda\]

Answer 1

@ganeshie8

Answer 2

u figured it out ? :)

Answer 3

\[(3i-j).(2i+\lambda j)=|3i-j|.|2i+\lambda j|\space cos\frac{\pi}{4} \]
\[6-\lambda =\sqrt{10}.\sqrt{4+\lambda^2}\times \frac{1}{\sqrt{2}}\]
\[6-\lambda =\sqrt{5}.\sqrt{4+\lambda^2}\]
\[(6-\lambda)^2 =5.(4+\lambda^2)^2\]

Answer 4

Am I correct ?

Answer 5

yes looks good, solve it all the way

Answer 6

ok :)

Answer 7

last step, i see a mistake
it should be :-

\((6-\lambda)^2 =5.(4+\lambda^2)\)

Answer 8

Ohh Yeah :)

Answer 9

Thanks for showing me.

Answer 10

np :) since its a quadratic, u wil get two values for lambda

Answer 11

\[\lambda^2-12\lambda+36=20+5\lambda^2\]
\[4\lambda^2+12\lambda-16=0\]
\[\lambda^2+3\lambda-4=0\]
\[\lambda^2+4\lambda-\lambda-4=0\]
\[(\lambda+4)(\lambda-1)=0\]
\[\lambda=-4 \space or \space \lambda=1\]

Answer 12

Hurray I got it :)

Answer 13

good job !!

Answer 14

Just bothered you with a mistake of mine.