A unit vector parallel to the resultant of the vectors A -4 -2 k- and B -3 -5 -k- isA- 4 -k-B- -4 -k-C- 4 -18-18-k-18D- -4 -18-18-k-18

The correct option is C 4 î√(18) ĵ√(18) k̂√(18)Resultant, R = A + B R = (î + 4ĵ 2 k̂) + (3î + 5ĵ k̂) R = 4î ĵ k̂ Unit vector along R̂ = R|R| R̂ = 4î ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

A unit vector...

Question

A unit vector parallel to the resultant of the vectors $\to A =^i + 4^j - 2^k$ and $\to B = 3^i - 5^j +^k$ is

4^i -^j -^k

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

\frac{4^i}{\sqrt{18}} - \frac{^j}{\sqrt{18}} - \frac{^k}{\sqrt{18}}

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

- \frac{4^i}{\sqrt{18}} + \frac{^j}{\sqrt{18}} + \frac{^k}{\sqrt{18}}

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

- 4^i +^j +^k

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

Open in App

Solution

The correct option is B $\frac{4^i}{\sqrt{18}} - \frac{^j}{\sqrt{18}} - \frac{^k}{\sqrt{18}}$
Resultant, $\to R = \to A + \to B$
$\to R = (^i + 4^j - 2^k) + (3^i + 5^j -^k)$
$\to R = 4^i -^j -^k$
Unit vector along $^R = \frac{\to R}{| \to R |}$
$^R = \frac{4^i -^j -^k}{\sqrt{4^{2} + (- 1)^{2} + (- 1)^{2}}}$
$^R = \frac{4^i}{\sqrt{18}} - \frac{^j}{\sqrt{18}} - \frac{^k}{\sqrt{18}}$

Suggest Corrections

Similar questions

Q. A unit vector perpendicular to both the vectors

2^i +^j + 3^k

and

2^i -^j +^k

Q. Let,

\to a =^i + 2^j +^k, \to b =^i -^j +^k, \to c =^i +^j -^k .

A vector coplanar to

\to a

and

\to b

has a projection along

\to c

of magnitude

\frac{1}{\sqrt{3}}

, then the vector is

With respect to a rectangular cartesian coordinate system, three vectors are expressed as $\to a = 4^i -^j, \to b = - 3^i + 2^j$ and
$\to c = -^k$ where $^i,^j,^k$ are unit vectors, along the X, Y and Z-axis respectively. The unit vectors $^r$ along the direction of sum of these vector is

Q. The incentre of the triangle formed by the points

^i +^j +^k,

4^i +^j +^k

, and

4^i + 5^j +^k

Q. Show that the four points A,B,C and D with position vectors

4^i + 5^j +^k, -^j -^k, 3^i + 9^j + 4^k and 4 (-^i +^j +^k)

respectively are coplanar.

Join BYJU'S Learning Program

A unit vector parallel to the resultant of the vectors →A=^i+4^j−2^k and →B=3^i−5^j+^k is

The correct option is B 4^i√18−^j√18−^k√18Resultant, →R=→A+→B →R=(^i+4^j−2^k)+(3^i+5^j−^k) →R=4^i−^j−^k Unit vector along ^R=→R|→R| ^R=4^i−^j−^k√42+(−1)2+(−1)2 ^R=4^i√18−^j√18−^k√18

A unit vector parallel to the resultant of the vectors $\to A =^i + 4^j - 2^k$ and $\to B = 3^i - 5^j +^k$ is