If a-4 -k- and b-2 -2 -k- then find a unit vector parallel to the vector a-b-

Here, we have a = 4î ĵ + k̂ and b = 2î 2ĵ+k̂ a+b= 4 î ĵ+k̂+2î 2ĵ+k̂ = 6î 3ĵ+2k̂ |a+b| = √((6)^2+( 3)^2+(2)^2) =√(36+9+4) = √(49)=7 A unit vector parallel ...

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

Byju's Answer

Standard XII

Mathematics

Angle between Two Vectors

If a⃗=4 î-ĵ+k...

Question

If $\to a = 4^i -^j +^k$ and $\to b = 2^i - 2^j +^k$ , then find a unit vector parallel to the vector $\to a + \to b$

Open in App

Solution

Here, we have $\to a = 4^i -^j +^k$ and $\to b = 2^i - 2^j +^k$

$\to a + \to b = 4^i -^j +^k + 2^i - 2^j +^k$

= $6^i - 3^j + 2^k$

$| \to a + \to b | = \sqrt{(6)^{2} + (- 3)^{2} + (2)^{2}}$

= $\sqrt{36 + 9 + 4} = \sqrt{49} = 7$

A unit vector parallel to the vector $\to a + \to b$

= $\frac{\to a + \to b}{| \to a + \to b |} = \frac{6^i - 3^j + 2^k}{7}$

= $\frac{1}{7} (6^i - 3^j + 2^k)$

Suggest Corrections

Similar questions

If $\to a = 4^i -^j +^k$ and $\to b = 2^i - 2^j +^k,$ then find a unit vector parallel to the vector $\to a + \to b$ .

Q. If

\to a =^i +^j +^k, \to b = 2^i -^j + 3^k

and

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

, find a unit vector parallel to the vector

2 \to a - \to b + 3 \to c

Q. If

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

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

, find a unit vectors normal to the vectors

\to a + \to b

and

\to b + \to c

Q. Given

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

and

\to c = -^i + 2^i -^k . A

unit vector perpendicular to both

\to a + \to b

\to b + \to c

Q. If

\to A = 3^i + 2^j

and

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

, then find a unit vector along

(\to A - \to B)

Join BYJU'S Learning Program

If →a=4^i−^j+^k and →b=2^i−2^j+^k, then find a unit vector parallel to the vector →a+→b

Here, we have →a=4^i−^j+^k and →b=2^i−2^j+^k →a+→b=4^i−^j+^k+2^i−2^j+^k = 6^i−3^j+2^k |→a+→b|=√(6)2+(−3)2+(2)2 =√36+9+4=√49=7 A unit vector parallel to the vector →a+→b =→a+→b|→a+→b|=6^i−3^j+2^k7 = 17(6^i−3^j+2^k)

If $\to a = 4^i -^j +^k$ and $\to b = 2^i - 2^j +^k$ , then find a unit vector parallel to the vector $\to a + \to b$