Let a-2-3-4k- and b-7-6k- If r-a-r-b- r-2-k-3- then r-2-3-k- is equal to-

Given : a=(2, 3, nbsp; 4), b=(7, 1, nbsp; 6) Now, nbsp; r×a=r×b ⇒r×a r×b=0 ⇒r× (a b)=0 ⇒r=λ (a b) ⇒ nbsp; nbsp;r=λ ( 5î 4ĵ+10k̂) We know that nbsp ...

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

Byju's Answer

Standard XII

Mathematics

Intersection of Sets

Let a=2î-3ĵ+4...

Question

Let $\to a = 2^i - 3^j + 4^k$ and $\to b = 7^i +^j - 6^k$ If $\to r \times \to a = \to r \times \to b, \to r \cdot (^i + 2^j +^k) = - 3,$ then $\to r \cdot (2^i - 3^j +^k)$ is equal to:

10

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

13

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

12

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

8

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

Open in App

Solution

The correct option is C $12$
Given : $\to a = (2, - 3, 4), \to b = (7, 1, - 6)$
Now,
$\to r \times \to a = \to r \times \to b \Rightarrow \to r \times \to a - \to r \times \to b = 0 \Rightarrow \to r \times (\to a - \to b) = 0 \Rightarrow \to r = λ (\to a - \to b) \Rightarrow \to r = λ (- 5^i - 4^j + 10^k)$

We know that
$\to r \cdot (1, 2, 1) = - 3 \Rightarrow λ (- 5 - 8 + 10) = - 3 \Rightarrow λ = 1$
$∴ (- 5, - 4, 10) \cdot (2, - 3, 1) = 12$

Suggest Corrections

Similar questions

Q. Let

x_{0}

be the point of Local maxima of

f (x) =

\to a \cdot (\to b \times \to c),

where

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

and

\to c = 7^i - 2^j + x^k

. Then the value of

\to a \cdot \to b + \to b \cdot \to c + \to c \cdot \to a

x = x_{0}

Q. If

\to a

and

\to b

are vectors such that

| \to a + \to b | = \sqrt{29}

and

\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b

, then a possible value of

(\to a + \to b) \cdot (- 7^i + 2^j + 3^k)

Q. If

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

and

\to c = r^i +^j + (2 r - 1)^k

are three vectors such that

\to c

is parallel to the plane of

\to a

and

\to b

, then r is equal to?

Q. Let

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

. If projection of

\to a

\to b

\frac{k}{\sqrt{29}}

, then the value of

(k - 2)

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}}

Join BYJU'S Learning Program

Let →a=2^i−3^j+4^k and →b=7^i+^j−6^k If →r×→a=→r×→b,→r⋅(^i+2^j+^k)=−3, then →r⋅(2^i−3^j+^k) is equal to:

The correct option is C 12Given : →a=(2,−3,4),→b=(7,1,−6) Now, →r×→a=→r×→b⇒→r×→a−→r×→b=0⇒→r×(→a−→b)=0⇒→r=λ(→a−→b)⇒→r=λ(−5^i−4^j+10^k) We know that →r⋅(1,2,1)=−3⇒λ(−5−8+10)=−3⇒λ=1 ∴(−5,−4,10)⋅(2,−3,1)=12

Let $\to a = 2^i - 3^j + 4^k$ and $\to b = 7^i +^j - 6^k$ If $\to r \times \to a = \to r \times \to b, \to r \cdot (^i + 2^j +^k) = - 3,$ then $\to r \cdot (2^i - 3^j +^k)$ is equal to: