Let a -2 -2 -k- and b be another vector such that - a - b -14 and - a - b -3 -8 k- then the vector b is equal toA- 5 -2 k-B- 5 -2 k- 5 -2 k-D- 3 -4 k-

The correct option is A 5î+ĵ+2k̂Let b=xî+yĵ+zk̂ Given a·b=14⇒2x+2y+z=141 a×b=3î+ĵ 8k̂ a×b=î amp;ĵ amp;k̂ 2 amp;2 amp;1 x amp;y amp;z=3î+ĵ 8k̂ 2z y= ...

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Byju's Answer

Standard XII

Mathematics

Equation of Plane Containing Two Lines

Let a =2 î+2 ...

Question

Let $\to a = 2^i + 2^j +^k$ and $\to b$ be another vector such that $\to a \cdot \to b = 14$ and $\to a \times \to b = 3^i +^j - 8^k$ then the vector $\to b$ is equal to

5^i +^j + 2^k

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5^i -^j - 2^k

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5^i +^j - 2^k

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3^i +^j + 4^k

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Solution

The correct option is A $5^i +^j + 2^k$
Let $\to b = x^i + y^j + z^k$
Given $\to a \cdot \to b = 14$ $\begin{matrix} \Rightarrow 2 x + 2 y + z = 14 \\ (1) \end{matrix}$
$\to a \times \to b = 3^i +^j - 8^k$
$\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 2 & 2 & 1 x & y & z \end{matrix} ∣ ∣ ∣ ∣ ∣ = 3^i +^j - 8^k$
$\begin{matrix} 2 z - y = 3 \Rightarrow y = 2 z - 3 \\ (2) \end{matrix}$
$\begin{matrix} - (2 z - x) = 1 \Rightarrow x = 2 z + 1 \\ (3) \end{matrix}$
Substitute equation $(2), (3)$ in equation $(1),$ we get
$z = 2, y = 1, x = 5$
$∴ \to b = 5^i +^j + 2^k$

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Similar questions

Q. A vector which makes equal angles with the vectors

\frac{1}{3} (^i - 2^j + 2^k), \frac{1}{5} (- 4^i - 3^k),^j .

Q. A vector which makes equal angles with the vectors

\frac{1}{3} (^i - 2^j + 2^k), \frac{1}{5} (- 4^i - 3^k),^j .

A = 3^i -^j + 7^k

and

B = 5^i -^j + 9^k

. The direction of the vector

A + B

Q. The unit vector which is perpendicular to the vectors

\to A =^i + 2^j -^k

and

\to B = 3^i - 2^j +^k

Q. Let

\to a = 2 \to 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

is equal to

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Let →a=2^i+2^j+^k and →b be another vector such that →a⋅→b=14 and →a×→b=3^i+^j−8^k then the vector →b is equal to

Let $\to a = 2^i + 2^j +^k$ and $\to b$ be another vector such that $\to a \cdot \to b = 14$ and $\to a \times \to b = 3^i +^j - 8^k$ then the vector $\to b$ is equal to