If the scalar projection of vector 2-x-k- on vector -2k- is 2-6- then the value of x is

Projection of vector 2î xĵ+k̂ on vector î+ĵ 2k̂ is (2î xĵ+k̂)·( î+ĵ 2k̂)√(1+1+4)=2√(6) ⇒ 4 x=2 ⇒ x= 6 nbsp; ...

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

Byju's Answer

Standard XII

Mathematics

Basic Inverse Trigonometric Functions

If the scalar...

Question

If the scalar projection of vector $2^i - x^j +^k$ on vector $-^i +^j - 2^k$ is $\frac{2}{\sqrt{6}},$ then the value of $x$ is

4

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

- 6

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

- 4

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

6

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

Open in App

Solution

The correct option is B $- 6$
Projection of vector $2^i - x^j +^k$ on vector $-^i +^j - 2^k$ is
$\frac{(2^i - x^j +^k) \cdot (-^i +^j - 2^k)}{\sqrt{1 + 1 + 4}} = \frac{2}{\sqrt{6}} \Rightarrow - 4 - x = 2 \Rightarrow x = - 6$

Suggest Corrections

Similar questions

Q. Let

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

be three vectors. A vector in the plane of

\to b

and

\to c

whose projection on

\to a

is of magnitude

\sqrt{\frac{2}{3}}

, is

Q. If

\to a = 2^i +^j +^k, \to b = 3^i - 4^j + 2^k, \to c =^i - 2^j + 2^k

then the projection of

\to a + \to b

\to c

Q. Suppose

{\to V}_{1} =^i +^j - 2^k, {\to V}_{2} =^i - 2^j +^k, {\to V}_{3} = - 2^i + 2^j +^k

are three vectors. Let

\to V

be a vector such that it can be expressed as a linear combination of

{\to V}_{1}

and

{\to V}_{2}

. Also

\to V {\to V}_{3} = 0

and the projection of the vector

\to V

^i -^j +^k

6 \sqrt{3}

. If

\to V = λ (^i + 3^j - 4^k)

then find the absolute value of

λ

\to a = - 2^i +^j +^k, \to b =^i + 5^j a n d \to c = 4^i + 4^j + 2^k

the projection of the vector

3 \to a - 2 \to b

on the vector

\to c

Q. Let

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

and a unit vector

\to c

be coplanar. If

\to c

is perpendicular to

\to a

, then

\to c =

Join BYJU'S Learning Program

Explore more

Basic Inverse Trigonometric Functions

Standard XII Mathematics

Join BYJU'S Learning Program

If the scalar projection of vector 2^i−x^j+^k on vector −^i+^j−2^k is 2√6, then the value of x is

The correct option is B −6Projection of vector 2^i−x^j+^k on vector −^i+^j−2^k is (2^i−x^j+^k)⋅(−^i+^j−2^k)√1+1+4=2√6⇒−4−x=2⇒x=−6

If the scalar projection of vector $2^i - x^j +^k$ on vector $-^i +^j - 2^k$ is $\frac{2}{\sqrt{6}},$ then the value of $x$ is

The correct option is B $- 6$
Projection of vector $2^i - x^j +^k$ on vector $-^i +^j - 2^k$ is
$\frac{(2^i - x^j +^k) \cdot (-^i +^j - 2^k)}{\sqrt{1 + 1 + 4}} = \frac{2}{\sqrt{6}} \Rightarrow - 4 - x = 2 \Rightarrow x = - 6$