If a-b-c form a left handed orthogonal system and a-a-4-b-b-9-c-c-16 then -a b c- is equal to

Given: a,b,c form a left handed orthogonal system. [a nbsp;b c ] = a· ( b×c) ⇒ |a| |b×c| cos180^0 n̂ (∵θ = 180^0 Left hand Orthogonal) ⇒ |a| |b×c| ⇒ |a| ...

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Standard XII

Physics

Introduction

If a,b,c form...

Question

If $\to a, \to b, \to c$ form a left handed orthogonal system and $\to a \cdot \to a = 4, \to b \cdot \to b = 9, \to c \cdot \to c = 16$ then $[\to a \to b \to c]$ is equal to

- 24

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Solution

The correct option is A $- 24$
Given: $\to a, \to b, \to c$ form a left handed orthogonal system. $[\to a \to b \to c] = \to a \cdot (\to b \times \to c)$
$\Rightarrow | \to a | | \to b \times \to c | cos 180^{0}^n (∵ θ = 180^{0} Left hand Orthogonal)$
$\Rightarrow - | \to a | | \to b \times \to c |$
$\Rightarrow - | \to a | | \to b | | \to c | sin 90^{0}$
$\Rightarrow - 2 \times 3 \times 4 \times 1 = - 24$

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¯ ¯ ¯ a \cdot ¯ ¯ ¯ a = ¯ ¯ b \cdot ¯ ¯ b = ¯ ¯ c \cdot ¯ ¯ c = 1, ¯ ¯ ¯ a \cdot ¯ ¯ b = \frac{1}{2}, ¯ ¯ b \cdot ¯ ¯ c = \frac{1}{\sqrt{2}} \cdot \to c \cdot ¯ ¯ ¯ a = \frac{\sqrt{3}}{2}

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If $¯ a, ¯ b, ¯ c$ form a left handed orthogonal system and $¯ a \cdot ¯ a = 4, ¯ b \cdot ¯ b = 9, ¯ c \cdot ¯ c$ =16 then $[¯ a ¯ b ¯ c]$ =

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Introduction

Standard XII Physics

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If →a,→b,→c form a left handed orthogonal system and →a⋅→a=4,→b⋅→b=9,→c⋅→c=16 then [→a →b →c] is equal to

The correct option is A −24Given: →a,→b,→c form a left handed orthogonal system. [→a →b →c]=→a⋅(→b×→c) ⇒|→a| |→b×→c|cos1800 ^n (∵θ=1800 Left hand Orthogonal) ⇒−|→a| |→b×→c| ⇒−|→a| |→b||→c|sin900 ⇒−2×3×4×1=−24

If $\to a, \to b, \to c$ form a left handed orthogonal system and $\to a \cdot \to a = 4, \to b \cdot \to b = 9, \to c \cdot \to c = 16$ then $[\to a \to b \to c]$ is equal to