Let V -2 i - j - k - W - i -3 k- if U is a unit vector then the maximum value of - U V W - isA- -33B- -59C- 7D- not defined

The correct option is B [ U̅, V̅, W̅ ]=U̅. ( V̅ .W̅ )=U̅. ( 3i 7j k ) = | U̅ | | 3i 7j k |cos θ =√(59)cosθ ∴Maximum value of [ U̅,V̅,W̅ ]=√(59). ( ∵ cos ...

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Byju's Answer

Standard XII

Mathematics

Complex Numbers

Let V =2 i + ...

Question

Let $\to V = 2 i + j - k, \to W = i + 3 k$ , if $\to U$ is a unit vector then the maximum value of [ $\to U \to V \to W$ ] is

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Solution

The correct option is C

$[¯ U, ¯ V, ¯ W] = ¯ U . (¯ V . ¯ W) = ¯ U . (3 i - 7 j - k) = ∣ ∣ ¯ U ∣ ∣ | 3 i - 7 j - k | c o s θ = \sqrt{59} c o s θ ∴ Maximum value of [¯ U, ¯ V, ¯ W] = \sqrt{59} . (∵ c o s θ \leq 1)$

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Let →V=2i+j−k,→W=i+3k, if →Uis a unit vector then the maximum value of [→U→V→W] is

The correct option is C [¯U,¯V,¯W]=¯U.(¯V .¯W)=¯U.(3i−7j−k)=∣∣¯U∣∣|3i−7j−k|cos θ=√59cosθ∴Maximum value of[¯U,¯V,¯W]=√59. (∵ cosθ≤1)

Let $\to V = 2 i + j - k, \to W = i + 3 k$ , if $\to U$ is a unit vector then the maximum value of [ $\to U \to V \to W$ ] is

The correct option is C

$[¯ U, ¯ V, ¯ W] = ¯ U . (¯ V . ¯ W) = ¯ U . (3 i - 7 j - k) = ∣ ∣ ¯ U ∣ ∣ | 3 i - 7 j - k | c o s θ = \sqrt{59} c o s θ ∴ Maximum value of [¯ U, ¯ V, ¯ W] = \sqrt{59} . (∵ c o s θ \leq 1)$