Let a-k- b-k- and c-k- be three vectors- A vector v in the plane of a and b- whose projection on c is 2-3- is given by

A vector v in the plane of a and b is v=a+λb v=(î+ĵ+k̂)+λ(î ĵ+k̂) Projection of v on c =2√(3) v.c|c|=2√(3) (1+λ) (1 λ) (1+λ)√(3)=2√(3) (1+λ) (1 λ) (1+λ)=2 λ=3 ...

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

Byju's Answer

Standard XI

Physics

Multiplication with Vectors

Let a=î+ĵ+k̂,...

Question

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 $\frac{2}{\sqrt{3}}$ , is given by

^i - 3^j + 3^k

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

- 3^i - 3^j -^k

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

3^i -^j + 3^k

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

4^i - 2^j + 4^k

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

Open in App

Solution

The correct option is D $4^i - 2^j + 4^k$
A vector $\to v$ in the plane of $\to a$ and $\to b$ is $\to v = \to a + λ \to b$
$⟹ \to v = (^i +^j +^k) + λ (^i -^j +^k)$
Projection of $\to v$ on $\to c$ = $\frac{2}{\sqrt{3}}$
$⟹ \frac{\to v . \to c}{∣ ∣ \to c ∣ ∣} = \frac{2}{\sqrt{3}}$
$⟹ \frac{(1 + λ) - (1 - λ) - (1 + λ)}{\sqrt{3}} = \frac{2}{\sqrt{3}}$
$⟹ (1 + λ) - (1 - λ) - (1 + λ) = 2$
$λ = 3$
So, $\to v = 4^i - 2^j + 4^k$

Suggest Corrections

Similar questions

Q. 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

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

, is given by

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

Q. Let

\to α =^i +^j +^k, \to β =^i -^j -^k; \to γ = -^i +^j -^k

be three vectors. A vector

\to δ

, in the plane of

\to α

and

\to β

, whose projection on

\to γ

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

, is given by

Join BYJU'S Learning Program

Let →a=^i+^j+^k, →b=^i−^j+^k and →c=^i−^j−^k be three vectors. A vector →v in the plane of →a and →b, whose projection on →c is 2√3, is given by

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 $\frac{2}{\sqrt{3}}$ , is given by