If r-r-r-k- and -r-2- then find r-A- 2-k-B- 2-3-k-C- 2-3-k-D- -3-k-

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

Multiplication with Vectors

If r⃗·î=r⃗·ĵ=...

Question

If $\to r .^i = \to r .^j = \to r .^k$ and $| r | = 2$ , then find $\to r$ .

2 (^i +^j +^k)

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

\frac{2}{3} (^i +^j +^k)

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

\frac{2}{\sqrt{3}} (^i +^j +^k)

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

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

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

Open in App

Solution

The correct option is C $\frac{2}{\sqrt{3}} (^i +^j +^k)$
Let $r = x^i + y^j + z^k$ .

Scalar product of a vector with a unit vector of x, y and z axis gives us the magnitude of vector in x, y and z direction i.e. the value of x, y and z.

Since, $\to r .^i = \to r .^j = \to r .^k \Rightarrow x = y = z \dots \dots (i)$
Also,
$| r | = 2 = \sqrt{x^{2} + y^{2} + z^{2}} = \sqrt{x^{2} + x^{2} + x^{2}} \sqrt{3 x^{2}} = 2 \sqrt{3} x = 2 x = \frac{2}{\sqrt{3}}$

Hence the required vector,
$\to r = \frac{2}{\sqrt{3}} (^i +^j +^k)$

Suggest Corrections

Similar questions

Q. If

\to r .^i = \to r .^j = \to r .^k

and

| r | = 3

, then find

\to r

Q. If

\to r .^i = \to r .^j = \to r .^k and | \to r | = 3, then \to r

is equal to

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

Q. The unit vector perpendicular to both

^i +^j

and

^j -^k

Q. The unit vector which, is perpendicular to the vectors

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

and

\to B = 3^i - 2^j -^k

Join BYJU'S Learning Program

If →r.^i=→r.^j=→r.^k and |r|=2, then find →r.

If $\to r .^i = \to r .^j = \to r .^k$ and $| r | = 2$ , then find $\to r$ .