The modulus of a vector A-5i-pj-4-2k- is 11- The value of p is-

The mean of the following data is 8.
$\begin{matrix} x & 3 & 5 & 7 & 9 & 11 & 13 y & 6 & 8 & 15 & p & 8 & 4 \end{matrix}$
then, the value of p is
(a) 23
(b) 24
(c) 25
(d) 21

Q. Equation of the plane through three points

A, B, C

with position vectors

- 6 \to i + 3 \to j + 2 \to k, 3 \to i - 2 \to j + 4 \to k, 5 \to i + 7 \to j + 3 \to k

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The modulus of a vector →A=5→i+p→j+4√2→k is 11. The value of p is:

The correct option is C ±8∣∣5¯i+p¯j+4√2¯¯¯k∣∣ =11⟹ (5)2+(p)2+(4√2)2=(11)2⟹(p)2 = 121−57 = 64⟹p=±8

The modulus of a vector $\to A = 5 \to i + p \to j + 4 \sqrt{2} \to k$ is 11. The value of p is:

The correct option is C $\pm 8$
$∣ ∣ \begin{matrix} 5 ¯ i + p ¯ j + 4 \sqrt{2} ¯ ¯ ¯ k \end{matrix} ∣ ∣$ $= 11$
$⟹$ $(5)^{2} + (p)^{2} + (4 \sqrt{2})^{2} = (11)^{2}$
$⟹ (p)^{2}$ $=$ $121 - 57$ $=$ $64$

$⟹ p = \pm 8$