If a-2-2k- then the value of -a- -2- - -a- -2- - k-a-k- -2 is equal to

|î×(a×î) |^2 = | (î·î)a nbsp; (a·î)î |^2 = | a 2î |^2 = |ĵ+2k̂ |^2 =5 Similarly, | ĵ×(a×ĵ) nbsp; |^2 = | a ĵ |^2 = |2î+2k̂ |^2 =8 and | k̂×(a×k̂) |^2 = | a ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Subtraction of a Vector

If a=2î+ĵ+2k̂...

Question

If $\to a = 2^i +^j + 2^k,$ then the value of ${∣ ∣^i \times (\to a \times^i) ∣ ∣}^{2} + {∣ ∣^j \times (\to a \times^j) ∣ ∣}^{2} + {∣ ∣^k \times (\to a \times^k) ∣ ∣}^{2}$ is equal to

Open in App

Solution

${∣ ∣^i \times (\to a \times^i) ∣ ∣}^{2}$
$= {∣ ∣ (^i \cdot^i) \to a - (\to a \cdot^i)^i ∣ ∣}^{2}$
$= {∣ ∣ \to a - 2^i ∣ ∣}^{2}$
$= {∣ ∣^j + 2^k ∣ ∣}^{2}$
$= 5$
Similarly,
${∣ ∣^j \times (\to a \times^j) ∣ ∣}^{2}$
$= {∣ ∣ \to a -^j ∣ ∣}^{2}$
$= {∣ ∣ 2^i + 2^k ∣ ∣}^{2}$
$= 8$
and ${∣ ∣^k \times (\to a \times^k) ∣ ∣}^{2}$
$= {∣ ∣ \to a - 2^k ∣ ∣}^{2}$
$= {∣ ∣ 2^i +^j ∣ ∣}^{2}$
$= 5$
Now,
${∣ ∣^i \times (\to a \times^i) ∣ ∣}^{2} + {∣ ∣^j \times (\to a \times^j) ∣ ∣}^{2} + {∣ ∣^k \times (\to a \times^k) ∣ ∣}^{2}$
$= 5 + 8 + 5 = 18$

Suggest Corrections

Similar questions

Q. If

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

then

{∣ ∣ (\to a \times^i) \times^j ∣ ∣}^{2} + {∣ ∣ (\to a \times^j) \times^k ∣ ∣}^{2} + {∣ ∣ (\to a \times^k) \times^i ∣ ∣}^{2} =

Q. A vector of magnitude

\sqrt{2}

coplanar with the vectors

\to a =^i +^j + 2^k

and

\to b =^i + 2^j +^k

and perpendicular to the vector

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

is
(1)

-^i -^k

(2)

^j -^k

(3)

^i -^j

(4)

^i +^k

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

Q. A unit vector in the plane of

^i + 2^j +^k

and

^i +^j + 2^k

and perpendicular to

2^i +^j +^k

, is

Q. A unit vector perpendicular to both the vectors

2^i +^j + 3^k

and

2^i -^j +^k

Join BYJU'S Learning Program

If →a=2^i+^j+2^k, then the value of ∣∣^i×(→a×^i)∣∣2+∣∣^j×(→a×^j)∣∣2+∣∣^k×(→a×^k)∣∣2 is equal to

If $\to a = 2^i +^j + 2^k,$ then the value of ${∣ ∣^i \times (\to a \times^i) ∣ ∣}^{2} + {∣ ∣^j \times (\to a \times^j) ∣ ∣}^{2} + {∣ ∣^k \times (\to a \times^k) ∣ ∣}^{2}$ is equal to