MyQuestionIcon

6

You visited us 6 times! Enjoying our articles? Unlock Full Access!

Test for Collinearity of Vectors

A unit vector...

Question

A unit vector parallel to $x y$ plane and perpendicular to the vector $4^i - 3^j +^k$ is

A

\pm \frac{(^i +^j +^k)}{\sqrt{3}}

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

B

\pm \frac{^i +^j}{5}

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

C

\pm \frac{3^i + 4^j}{5}

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

D

\pm \frac{3^i - 4^j}{5}

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

Open in App

Solution

The correct option is C $\pm \frac{3^i + 4^j}{5}$
$\begin{matrix} L e t t h e v e c t o r b e x^i + y^j (x^i + y^j) . (4^i - 3^j +^k) = 0 4 x - 3 y = 0 x^{2} + y^{2} = 1 x^{2} + \frac{16 x^{2}}{9} = 1 \frac{25 x^{2}}{9} = 1 x = \pm \frac{3}{5} x = \frac{3}{5}, y = \frac{4}{5} x = \frac{- 3}{5}, y = \frac{- 4}{5} R e q u i r e d v e c t o r = \pm \frac{3^i + 4^j}{5} H e n c e, t h e o p t i o n C i s c o r r e c t . \end{matrix}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A unit vector parallel to the resultant of the vectors

\to A =^i + 4^j - 2^k

\to B = 3^i - 5^j +^k

Q. The unit vector perpendicular to both of the vectors 2

^i -^j +^k

3^i + 4^j -^k

\to a =^i +^j +^k

\to b =^i -^j +^k

\to c =^i -^j -^k

be three vectors. A vector

\to v

in the plane of

\to a

\to b

, whose projection on

\to c

\frac{2}{\sqrt{3}}

Q. The unit vector perpendicular to both

^i +^j

^j -^k

Let $\to a =^i +^j +^k, \to b =^i -^j +^k$ and $\to c =^i -^j -^k$ be three vectors. A vector $\to v$ in the plane of
$\to a$ and $\to b$ , whose projection on $\to c$ is $\frac{1}{\sqrt{3}}$ , is given by

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Test for Collinearity of 3 Points or 2 Vectors

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Test for Collinearity of Vectors

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon