Let a- b- and c- be 3 mutually perpendicular unit vectors- If d- is a unit vector which is equally inclined to a- b- and c- then the value of -a- b - c - d -2 is p - q then p - q is

Since, the vector nbsp;d is a unit vector which is equally inclined to a, b and c ⇒d=a+b+c/√(3) d.a=d.b=d.c=1/√(3) |a+b+c+d|^2=|a+b+c|^2+|d|^2+2 d.(a+b+c) ...

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Byju's Answer

Standard XII

Physics

Comparing Vectors

Let a⃗, b⃗ an...

Question

Let $\to a$ , $\to b$ and $\to c$ be 3 mutually perpendicular unit vectors. If $\to d$ is a unit vector which is equally inclined to $\to a$ , $\to b$ and $\to c$ , then the value of $| \to a + \to b + \to c + \to d |^{2}$ is $p + \sqrt{q}$ then $p + q$ is

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Solution

Since, the vector $\to d$ is a unit vector which is equally inclined to $\to a$ , $\to b$ and $\to c$
$\Rightarrow \to d = \frac{\to a + \to b + \to c}{\sqrt{3}}$

$\to d . \to a = \to d . \to b = \to d . \to c = \frac{1}{\sqrt{3}}$

$| \to a + \to b + \to c + \to d |^{2} = | \to a + \to b + \to c |^{2} + | \to d |^{2} + 2 \to d . (\to a + \to b + \to c)$

$= 3 + 1 + 2 \times (\frac{3}{\sqrt{3}})$

$= 4 + 2 \sqrt{3}$

$= 4 + \sqrt{12}$

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Let →a, →b and →c be 3 mutually perpendicular unit vectors. If →d is a unit vector which is equally inclined to →a, →b and →c, then the value of |→a+→b+→c+→d|2 is p+√q then p+q is

Since, the vector →d is a unit vector which is equally inclined to →a, →b and →c ⇒→d=→a+→b+→c√3 →d.→a=→d.→b=→d.→c=1√3 |→a+→b+→c+→d|2=|→a+→b+→c|2+|→d|2+2→d.(→a+→b+→c) =3+1+2×(3√3) =4+2√3 =4+√12

Let $\to a$ , $\to b$ and $\to c$ be 3 mutually perpendicular unit vectors. If $\to d$ is a unit vector which is equally inclined to $\to a$ , $\to b$ and $\to c$ , then the value of $| \to a + \to b + \to c + \to d |^{2}$ is $p + \sqrt{q}$ then $p + q$ is