Let a -2 -3 -6 k- b -2 -3 -6 k- and c -2 -3 -6 k- Let a 1 be the projection of a on b and a 2 be the projection of a 1on c- Then- a 2 is equal toA- 943-4922 -3 -6 k- 943-49-2 -3 -6 k-C- 943-492-2 -3 -6 k-D- g 43-492 -3 -6 k-

The correct option is A 94349^2(2î 3ĵ 6k̂) nbsp;a_1=[(2î+3ĵ 6k̂) ·(2î 3ĵ+6k̂)7] (2î 3ĵ+6k̂)7 ⇒a_1= 4149(2î 3ĵ+6k̂) a_2= 4149[(2î 3ĵ+6k̂) ·( 2î+3ĵ+6k̂)7] ( 2 ...

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

Byju's Answer

Standard XII

Mathematics

Applications of Dot Product

Let a =2 î+3 ...

Question

Let $\to a = 2^i + 3^j - 6^k, \to b = 2^i - 3^j + 6^k$ and $\to c = - 2^i + 3^j + 6^k$ . Let ${\to a}_{1}$ be the projection of $\to a$ on $\to b$ and ${\to a}_{2}$ be the projection of ${\to a}_{1}$ on $\to c$ . Then, ${\to a}_{2}$ is equal to

\frac{943}{49} (2^i - 3^j - 6^k)

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

\frac{943}{49^{2}} (2^i - 3^j - 6^k)

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

\frac{943}{49} (- 2^i + 3^j + 6^k)

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

\frac{943}{49^{2}} (- 2^i + 3^j + 6^k)

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

Open in App

Solution

The correct option is B $\frac{943}{49^{2}} (2^i - 3^j - 6^k)$
$_{1} = [(2^i + 3^j - 6^k) \cdot \frac{(2^i - 3^j + 6^k)}{7}] \frac{(2^i - 3^j + 6^k)}{7}$
$\Rightarrow_{1} = - \frac{41}{49} (2^i - 3^j + 6^k)$

$_{2} = - \frac{41}{49} [(2^i - 3^j + 6^k) \cdot \frac{(- 2^i + 3^j + 6^k)}{7}] \frac{(- 2^i + 3^j + 6^k)}{7}$

$\Rightarrow_{2} = - \frac{41}{(49)^{2}} (- 4 - 9 + 36) (- 2^i + 3^j + 6^k)$

$\Rightarrow_{2} = \frac{943}{(49)^{2}} (2^i - 3^j - 6^k)$

Suggest Corrections

Similar questions

Q. Let

\to a = 2^i + 3^j - 6^k, \to b = 2^i - 3^j + 6^k

and

\to c = - 2^i + 3^j + 6^k

. Let

{\to a}_{1}

be the projection of

\to a

\to b

and

{\to a}_{2}

be the projection of

{\to a}_{1}

\to c

. Then,

{\to a}_{1} . \to b

is equal to

Q. Let

\to a = 2^i + 3^j - 6^k, \to b = 2^i - 3^j + 6^k

and

\to c = - 2^i + 3^j + 6^k

. Let

{\to a}_{1}

be the projection of

\to a

\to b

and

{\to a}_{2}

be the projection of

{\to a}_{1}

\to c

. Then,

{\to a}_{2}

is equal to

Q. Let

\to a = 2^i + 3^j - 6^k, \to b = 2^i - 3^j + 6^k

and

\to c = - 2^i + 3^j + 6^k

. Let

{\to a}_{1}

be the projection of

\to a

\to b

and

{\to a}_{2}

be the projection of

{\to a}_{1}

\to c

. Then, which of the following is true?

Q. Find the scalar projection of the vector

^i + 3^j + 7^k

on the vector

2^i - 3^j + 6^k .

Q. A unit vector perpendicular to the plane of

a = 2^i - 6^j - 3^k, b = 4^i + 3^j -^k

Join BYJU'S Learning Program

Let →a=2^i+3^j−6^k, →b=2^i−3^j+6^k and →c=−2^i+3^j+6^k. Let →a1 be the projection of →a on →b and →a2 be the projection of →a1 on →c. Then, →a2 is equal to

The correct option is B 943492(2^i−3^j−6^k) →a1=[(2^i+3^j−6^k)⋅(2^i−3^j+6^k)7](2^i−3^j+6^k)7 ⇒→a1=−4149(2^i−3^j+6^k) →a2=−4149[(2^i−3^j+6^k)⋅(−2^i+3^j+6^k)7](−2^i+3^j+6^k)7 ⇒→a2=−41(49)2(−4−9+36)(−2^i+3^j+6^k) ⇒→a2=943(49)2(2^i−3^j−6^k)

Let $\to a = 2^i + 3^j - 6^k, \to b = 2^i - 3^j + 6^k$ and $\to c = - 2^i + 3^j + 6^k$ . Let ${\to a}_{1}$ be the projection of $\to a$ on $\to b$ and ${\to a}_{2}$ be the projection of ${\to a}_{1}$ on $\to c$ . Then, ${\to a}_{2}$ is equal to