If f(x)=(\cos x) \stackrel{\^}{i}+(\sin x) \stackrel{\^}{j}+(\cos 2 x) {k^{\^}}, g(x) =(\tan x) \stackrel{\^}{i}+(\sin 3 x) \stackrel{\^}{j}+(\cos 4 x) \stackrel{\^}{k} andh(x)=(\cos 3 x) \stackrel{\^}{i}+(\sin 5 x) \stackrel{\^}{j}+(\cos 6 x) \stackrel{\^}{k} are three variable vectors given, then\\int_{0} ^{\\pi}[f(x), g(x), h(x)] d x, where [.] denotes scalar triple product, is equal to

JEE Advanced 2021 Full Test 3 Paper 2

SECTION – C (Numerical Answer Type)
This section contains 06 questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value (in decimal notation, truncated/rounded-off to the SECOND DECIMAL PLACE; e.g. XXXXX. XX).

Question : 51 of 54

Marks: +1, -0

If f(x)=(cos‌x)

+(sin‌x)

+(cos‌2‌x)

, g(x)=(tan‌x)

+(sin‌3‌x)

+(cos‌4‌x)

andh(x)=(cos‌3‌x)

+(sin‌5‌x)

+(cos‌6‌x)

are three variable vectors given, then

∫

[f(x),g(x),h(x)]dx, where [.] denotes scalar triple product, is equal to

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cos‌x	sin‌x	cos‌2‌x
tan‌x	sin‌3‌x	cos‌4‌x
cos‌3‌x	sin‌5‌x	cos‌6‌x