You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Shortest Distance between Two Skew Lines

The unit vect...

Question

The unit vector bisecting $O Y$ and $O Z$ is

\frac{^i +^j +^k}{\sqrt{3}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{^j + 2^k}{\sqrt{5}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{2^j -^k}{\sqrt{5}}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

\frac{^j +^k}{\sqrt{2}}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $\frac{^j +^k}{\sqrt{2}}$
$^j,^k$ are unit vector along $Y, Z$ axes
We know $- - \to O Y =^j, - - \to O Z =^k$
Vector bisecting $- - \to O Y, - - \to O Z$ is $\to N = λ (^j \pm^k)$
Hence, unit vector bisecting will be $^N = \frac{^j \pm^k}{\sqrt{2}}$

Suggest Corrections

Similar questions

Q. The vector equations of OX, OY and OZ are ______________.

Let O be the origin and OX, OY, OZ be three unit vectors in the directions of the sides QR, RP, PQ respectively, of a triangle PQR.
$| O X \times O Y | =$

Q. Let

O

be the origin, and

- - \to O X, - - \to O Y, - - \to O Z

be three unit vectors in the directions of the sides

- - \to Q R, - - \to R P, - - \to P Q,

respectively, of a triangle

P Q R .

| - - \to O X \times - - \to O Y | =

Show that the vector is equally inclined to the axes OX, OY, and OZ.

Q. Show that the vector is equally inclined to the axes OX, OY, and OZ.

Join BYJU'S Learning Program

Explore more

Shortest Distance between Two Skew Lines

Standard XII Mathematics

Join BYJU'S Learning Program

The unit vector bisecting OY and OZ is

The correct option is D ^j+^k√2^j, ^k are unit vector along Y,Z axes We know −−→OY=^j, −−→OZ=^k Vector bisecting −−→OY,−−→OZ is →N=λ(^j±^k) Hence, unit vector bisecting will be ^N=^j±^k√2

The unit vector bisecting $O Y$ and $O Z$ is

The correct option is D $\frac{^j +^k}{\sqrt{2}}$
$^j,^k$ are unit vector along $Y, Z$ axes
We know $- - \to O Y =^j, - - \to O Z =^k$
Vector bisecting $- - \to O Y, - - \to O Z$ is $\to N = λ (^j \pm^k)$
Hence, unit vector bisecting will be $^N = \frac{^j \pm^k}{\sqrt{2}}$