If a unit vector a makes angle -3 with - -4 with - and an acute angle - with k- then find the value of -

If a unit vector $^a$ , makes angles $\frac{π}{3}$ with $^i, \frac{π}{4}$ with $^j$ and an acute angle $θ$ with $^k$ , then find $θ$ and hence the components of a.

Q. If a unit vector

¯ a

makes angles

\frac{π}{3}

with

^i

\frac{π}{4}

with

^j

and an acute angle

θ

with

^k

, find

θ

and hence, the component of

\to a

Q. If a unit vector

\to a

makes an angle

\frac{π}{3}

with

^i

\frac{π}{4}

with

^j

and

θ \in (0, π)

with

^k

, then a value of

θ

is :

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If a unit vector →a makes angle π3 with ^i,π4 with ^j and an acute angle θ with ^k, then find the value of θ.

Let α be an angle formed by vector with i and β be an angle formed by j and θ be an angle formed by vector k.Now as rule states,cos2α+cos2β+cos2θ=1⇒cos2(π3)+cos2(π4)+cos2θ=1⇒14+12+cos2θ=1cos2θ=1−14−12=1−34=14cosθ=√14cosθ=12THerefore, θ=cos−1(12)=π3

If a unit vector $\to a$ makes angle $\frac{π}{3}$ with $^i, \frac{π}{4}$ with $^j$ and an acute angle $θ$ with $^k$ , then find the value of $θ$ .