Find value of a with given angle
$begingroup$
The equations of the line $L$ and the plane $Pi$ are as follows:
$$
L: qquad x-5=-(y+1); z = 4
$$
$$
Pi : qquad alpha x + z = 5alpha +4
$$
where $alpha$ is a constant.
If the angle between the line $L$ and $Pi$ is $pi/6$, what is the value of $alpha$?
There are two answers, one positive and negative, but the answers I got is only negative. Any help please. Thanking you guys in advanced :D
geometry
edited Jan 17 at 13:15
idriskameni
749321
asked Jan 17 at 13:00
Master Irfan ElaheeMaster Irfan Elahee
13
$endgroup$
add a comment |
$begingroup$
The equations of the line $L$ and the plane $Pi$ are as follows:
$$
L: qquad x-5=-(y+1); z = 4
$$
$$
Pi : qquad alpha x + z = 5alpha +4
$$
where $alpha$ is a constant.
If the angle between the line $L$ and $Pi$ is $pi/6$, what is the value of $alpha$?
There are two answers, one positive and negative, but the answers I got is only negative. Any help please. Thanking you guys in advanced :D
geometry
edited Jan 17 at 13:15
idriskameni
749321
asked Jan 17 at 13:00
Master Irfan ElaheeMaster Irfan Elahee
13
$endgroup$
2
$begingroup$
can you include your working?
$endgroup$
– Siong Thye Goh
Jan 17 at 13:02
$begingroup$
@SiongThyeGoh ibb.co/6t3PkD1 sorry the answer i got was a negative
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:06
1
$begingroup$
please learn mathjax and type out your attempt in the question.
$endgroup$
– Siong Thye Goh
Jan 17 at 13:23
$begingroup$
will do :D thanks
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:29
add a comment |
$begingroup$
The equations of the line $L$ and the plane $Pi$ are as follows:
$$
L: qquad x-5=-(y+1); z = 4
$$
$$
Pi : qquad alpha x + z = 5alpha +4
$$
where $alpha$ is a constant.
If the angle between the line $L$ and $Pi$ is $pi/6$, what is the value of $alpha$?
There are two answers, one positive and negative, but the answers I got is only negative. Any help please. Thanking you guys in advanced :D
geometry
edited Jan 17 at 13:15
idriskameni
749321
asked Jan 17 at 13:00
Master Irfan ElaheeMaster Irfan Elahee
13
$endgroup$
The equations of the line $L$ and the plane $Pi$ are as follows:
$$
L: qquad x-5=-(y+1); z = 4
$$
$$
Pi : qquad alpha x + z = 5alpha +4
$$
where $alpha$ is a constant.
If the angle between the line $L$ and $Pi$ is $pi/6$, what is the value of $alpha$?
There are two answers, one positive and negative, but the answers I got is only negative. Any help please. Thanking you guys in advanced :D
geometry
geometry
edited Jan 17 at 13:15
idriskameni
749321
asked Jan 17 at 13:00
Master Irfan ElaheeMaster Irfan Elahee
13
edited Jan 17 at 13:15
idriskameni
749321
asked Jan 17 at 13:00
Master Irfan ElaheeMaster Irfan Elahee
13
edited Jan 17 at 13:15
idriskameni
749321
edited Jan 17 at 13:15
idriskameni
749321
edited Jan 17 at 13:15
idriskameni
749321
749321
asked Jan 17 at 13:00
Master Irfan ElaheeMaster Irfan Elahee
13
asked Jan 17 at 13:00
Master Irfan ElaheeMaster Irfan Elahee
13
asked Jan 17 at 13:00
Master Irfan ElaheeMaster Irfan Elahee
13
13
2
$begingroup$
can you include your working?
$endgroup$
– Siong Thye Goh
Jan 17 at 13:02
$begingroup$
@SiongThyeGoh ibb.co/6t3PkD1 sorry the answer i got was a negative
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:06
1
$begingroup$
please learn mathjax and type out your attempt in the question.
$endgroup$
– Siong Thye Goh
Jan 17 at 13:23
$begingroup$
will do :D thanks
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:29
add a comment |
2
$begingroup$
can you include your working?
$endgroup$
– Siong Thye Goh
Jan 17 at 13:02
$begingroup$
@SiongThyeGoh ibb.co/6t3PkD1 sorry the answer i got was a negative
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:06
1
$begingroup$
please learn mathjax and type out your attempt in the question.
$endgroup$
– Siong Thye Goh
Jan 17 at 13:23
$begingroup$
will do :D thanks
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:29
2
2
$begingroup$
can you include your working?
$endgroup$
– Siong Thye Goh
Jan 17 at 13:02
$begingroup$
can you include your working?
$endgroup$
– Siong Thye Goh
Jan 17 at 13:02
$begingroup$
@SiongThyeGoh ibb.co/6t3PkD1 sorry the answer i got was a negative
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:06
$begingroup$
@SiongThyeGoh ibb.co/6t3PkD1 sorry the answer i got was a negative
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:06
1
1
$begingroup$
please learn mathjax and type out your attempt in the question.
$endgroup$
– Siong Thye Goh
Jan 17 at 13:23
$begingroup$
please learn mathjax and type out your attempt in the question.
$endgroup$
– Siong Thye Goh
Jan 17 at 13:23
$begingroup$
will do :D thanks
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:29
$begingroup$
will do :D thanks
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:29
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
$$L:begin{pmatrix} x \ y \ zend{pmatrix}=begin{pmatrix} 5 \ -1 \ 4end{pmatrix}+ lambda begin{pmatrix}1 \ -1\ 0 end{pmatrix}$$
$$frac{|langle(1,-1,0),(alpha, 0,1)rangle|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
$$frac{|alpha|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
Hopefully you can solve for $alpha$ to obtain one positive and one negative value of $alpha$ from here.
answered Jan 17 at 13:20
Siong Thye GohSiong Thye Goh
104k1468120
$endgroup$
add a comment |
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1 Answer
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1 Answer
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$begingroup$
$$L:begin{pmatrix} x \ y \ zend{pmatrix}=begin{pmatrix} 5 \ -1 \ 4end{pmatrix}+ lambda begin{pmatrix}1 \ -1\ 0 end{pmatrix}$$
$$frac{|langle(1,-1,0),(alpha, 0,1)rangle|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
$$frac{|alpha|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
Hopefully you can solve for $alpha$ to obtain one positive and one negative value of $alpha$ from here.
answered Jan 17 at 13:20
Siong Thye GohSiong Thye Goh
104k1468120
$endgroup$
add a comment |
$begingroup$
$$L:begin{pmatrix} x \ y \ zend{pmatrix}=begin{pmatrix} 5 \ -1 \ 4end{pmatrix}+ lambda begin{pmatrix}1 \ -1\ 0 end{pmatrix}$$
$$frac{|langle(1,-1,0),(alpha, 0,1)rangle|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
$$frac{|alpha|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
Hopefully you can solve for $alpha$ to obtain one positive and one negative value of $alpha$ from here.
answered Jan 17 at 13:20
Siong Thye GohSiong Thye Goh
104k1468120
$endgroup$
add a comment |
$begingroup$
$$L:begin{pmatrix} x \ y \ zend{pmatrix}=begin{pmatrix} 5 \ -1 \ 4end{pmatrix}+ lambda begin{pmatrix}1 \ -1\ 0 end{pmatrix}$$
$$frac{|langle(1,-1,0),(alpha, 0,1)rangle|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
$$frac{|alpha|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
Hopefully you can solve for $alpha$ to obtain one positive and one negative value of $alpha$ from here.
answered Jan 17 at 13:20
Siong Thye GohSiong Thye Goh
104k1468120
$endgroup$
$$L:begin{pmatrix} x \ y \ zend{pmatrix}=begin{pmatrix} 5 \ -1 \ 4end{pmatrix}+ lambda begin{pmatrix}1 \ -1\ 0 end{pmatrix}$$
$$frac{|langle(1,-1,0),(alpha, 0,1)rangle|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
$$frac{|alpha|}{sqrt2cdot sqrt{alpha^2+1}}=cosfrac{pi}6$$
Hopefully you can solve for $alpha$ to obtain one positive and one negative value of $alpha$ from here.
answered Jan 17 at 13:20
Siong Thye GohSiong Thye Goh
104k1468120
answered Jan 17 at 13:20
Siong Thye GohSiong Thye Goh
104k1468120
answered Jan 17 at 13:20
Siong Thye GohSiong Thye Goh
104k1468120
answered Jan 17 at 13:20
Siong Thye GohSiong Thye Goh
104k1468120
104k1468120
add a comment |
add a comment |
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$begingroup$
can you include your working?
$endgroup$
– Siong Thye Goh
Jan 17 at 13:02
$begingroup$
@SiongThyeGoh ibb.co/6t3PkD1 sorry the answer i got was a negative
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:06
1
$begingroup$
please learn mathjax and type out your attempt in the question.
$endgroup$
– Siong Thye Goh
Jan 17 at 13:23
$begingroup$
will do :D thanks
$endgroup$
– Master Irfan Elahee
Jan 17 at 13:29