If a-k- and b-2 -k- then z - component of a vector r- which is coplanar with a- and b- r-b-0 and r-a-7 is

R=pa+qb Given that nbsp;r. b = 0 & r. a = 7 ⇒ p=5/2 & q=1/2 ⇒r=( 3/2, 5/2, 3) ...

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Byju's Answer

Standard XII

Mathematics

Angle between a Plane and a Line

If a⃗=-î+ĵ+k̂...

Question

If $\to a = -^i +^j +^k$ and $\to b = 2^i +^k$ , then $z$ - component of a vector $\to r$ which is coplanar with $\to a$ and $\to b, \to r . \to b = 0$ and $\to r . \to a = 7$ is

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Solution

$\to r = p \to a + q \to b$
Given that $\to r . \to b = 0 & \to r . \to a = 7$
$\Rightarrow p = \frac{5}{2} & q = \frac{1}{2} \Rightarrow \to r = (- \frac{3}{2}, \frac{5}{2}, 3)$

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If →a=−^i+^j+^k and →b=2^i+^k, then z - component of a vector →r which is coplanar with →a and →b,→r.→b=0 and →r.→a=7 is

→r=p→a+q→b Given that →r.→b=0 & →r.→a=7 ⇒p=52 & q=12⇒→r=(−32,52,3)

If $\to a = -^i +^j +^k$ and $\to b = 2^i +^k$ , then $z$ - component of a vector $\to r$ which is coplanar with $\to a$ and $\to b, \to r . \to b = 0$ and $\to r . \to a = 7$ is

$\to r = p \to a + q \to b$
Given that $\to r . \to b = 0 & \to r . \to a = 7$
$\Rightarrow p = \frac{5}{2} & q = \frac{1}{2} \Rightarrow \to r = (- \frac{3}{2}, \frac{5}{2}, 3)$