If a-2-1-1-b-1-1-0-c-5-1-1- then the unit vector parallel to a-b-c in the opposite direction is

Given a=(2,1, 1),b=(1, 1,0),c=(5, 1,1) a+b c=(2î+ĵ k̂ )+(î ĵ+0k̂) (5î ĵ+k̂) a+b c= 2 î +ĵ 2k̂ Magnitude of the vector is √(4+1+4)=3 So the unit vector in the o ...

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

Byju's Answer

Standard X

Mathematics

Section Formula

If a=2,1,-1,b...

Question

If $\to a = (2, 1, - 1), \to b = (1, - 1, 0), \to c = (5, - 1, 1),$ then the unit vector parallel to $\to a + \to b - \to c$ in the opposite direction is

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

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

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

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

(\frac{-^i + 2^j -^k}{\sqrt{6}})

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

(\frac{^i - 2^j +^k}{\sqrt{6}})

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

Open in App

Solution

The correct option is B $(\frac{2^i -^j + 2^k}{3})$
Given $\to a = (2, 1, - 1), \to b = (1, - 1, 0), \to c = (5, - 1, 1)$
$\to a + \to b - \to c = (2^i +^j -^k) + (^i -^j + 0^k) - (5^i -^j +^k)$
$\to a + \to b - \to c = - 2^i +^j - 2^k$
Magnitude of the vector is $\sqrt{4 + 1 + 4} = 3$
So the unit vector in the opposite direction $= - (\frac{- 2^i +^j - 2^k}{3})$
$∴$ Required unit vector $= (\frac{2^i -^j + 2^k}{3})$

Suggest Corrections

Similar questions

I f \to a =< 3, - 2, 1 > \to b =< - 1, 1, 1 >

then the unit vector parallel to the vector

\to a + \to b

I f \to a = (3, - 2, 1), \to b = (- 1, 1, 1)

then the unit vector parallel to the vector

\to a + \to b

I f \to a =< 3, - 2, 1 > \to b =< - 1, 1, 1 >

then the unit vector parallel to the vector

\to a + \to b

Q. If

\to a, \to b

and

\to c

are unit vectors satisfying

| \to a - \to b |^{2} + | \to b - \to c |^{2} + | \to c - \to a |^{2} = 9,

then

| 2 \to a + 5 \to b + 5 \to c |

Q. If

^{1},^{1},^{1}

is the reciprocal system of vector triad of

\to a, \to b, \to c

, then

\to a .^{1} + \to b .^{1} + \to c .^{1} =

Join BYJU'S Learning Program

Explore more

Section Formula

Standard X Mathematics

Join BYJU'S Learning Program

If →a=(2,1,−1),→b=(1,−1,0),→c=(5,−1,1), then the unit vector parallel to →a+→b−→c in the opposite direction is

If $\to a = (2, 1, - 1), \to b = (1, - 1, 0), \to c = (5, - 1, 1),$ then the unit vector parallel to $\to a + \to b - \to c$ in the opposite direction is