Let a = i ^ + j ^ + 2 k ^ and b = 2 i ^ − j ^ + k ^ . If unit vector c maximizes [ a b c ] at M , which statements are true?

The maximum is ∣ a × b ∣ = 3 3 , attained for c = ( a × b ) /∣ a × b ∣ = ( i ^ + j ^ − k ^ ) / 3 .

Start Free Mock LoginAlready registered? Login here

Mathematics - Vector Question with Solution | TestHub

MathematicsVectorVTPMedium2 minQB

MathematicsMediummultiple choice

Let $a = \hat{i} + \hat{j} + 2 \hat{k}$ and $b = 2 \hat{i} - \hat{j} + \hat{k}$ . If unit vector $c$ maximizes $[a b c]$ at $M$ , which statements are true?

Options:(select one or more)

Answer:

A, C

Solution:

The maximum is $∣ a \times b ∣ = 33$ , attained for $c = (a \times b) /∣ a \times b ∣ = (\hat{i} + \hat{j} - \hat{k}) / 3$ .

Stream:JEESubject:MathematicsTopic:VectorSubtopic:VTP

⏱ 2mℹ️ Source: QB

Doubts & Discussion

Loading discussions...