Let- a- - - - 2 - -k-b- - - - - - k- -c- - - - - - k- A vector coplanar to a- and b- has a projection along c- of magnitude 1-3- then the vector is2- - - - k-4- - - - 4k-4- - - - 4kNone of these

The correct option is B 4î ĵ + 4k̂Let vector r⃗ be coplanar to a⃗ and b⃗. ∴r⃗ = a⃗ + t b⃗ ⇒r⃗ = (î + 2ĵ + k̂) + t (î ĵ + k̂) = î (1 + t) + ĵ (2 t) + k̂ (1 ...

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

Byju's Answer

Standard IX

Mathematics

Linear Combination of Vectors

Let, a⃗ = î +...

Question

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

4^i -^j + 4^k

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

4^i +^j - 4 k

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

2^i +^j +^k

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

None of these

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

Open in App

Solution

The correct option is A $4^i -^j + 4^k$
Let vector $\to r$ be coplanar to $\to a$ and $\to b . ∴ \to r = \to a + t \to b \Rightarrow \to r = (^i + 2^j +^k) + t (^i -^j +^k) =^i (1 + t) +^j (2 - t) +^k (1 + t)$
The projection of $\to r$ on $\to c = \frac{1}{\sqrt{3} .}$ [given]
$\Rightarrow \frac{\to r . \to c}{| \to c |} = \frac{1}{\sqrt{3}} \Rightarrow \frac{| 1. (1 + t) + 1. (2 - t) - 1. (1 + t) |}{\sqrt{3}} = \frac{1}{\sqrt{3}}$
$\Rightarrow (2 - t) = \pm 1 \Rightarrow t = 1 o r 3$
When, t = 1, we have $\to r = 2^i +^j + 2^k$
When, t = 3, we have $\to r = 4^i -^j + 4^k$

Suggest Corrections

Similar questions

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

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

Q. If

\to a =^i +^j +^k

\to b =^i -^j +^k

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

and

\to a =^i -^j -^k

, then

(\to a \times \to b) \times (\to c \times \to d)

is a vector orthogonal to both

Q. Let

\to a

= 2

^i

^j

^k

\to b

^i

+ 2

^j

^k

and

\to c

^i

^j

^k

be three vector . A vector in plane of

\to b

and

\to c

, whose projection on

\to a

is a magnitude

\sqrt{2 / 3}

, is

Q. If

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

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

and

\to d =^i -^j -^k

, then

(\to a \times \to b) \times (\to c \times \to d) =

Join BYJU'S Learning Program

Let, →a=^i+2^j+^k, →b=^i−^j+^k, →c=^i+^j−^k. A vector coplanar to →a and →b has a projection along →c of magnitude 1√3, then the vector is

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