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← JEE Main 2022 · 25 Jul · Shift 2
MathematicsSingle correct+4 / -1Question 17 of 90

JEE Main 2022 · 25 Jul · Shift 2, Mathematics question 17

Let a⃗=i^−j^+2k^\vec a=\hat i-\hat j+2\hat k and let b⃗\vec b be a vector such that a⃗×b⃗=2i^−k^\vec a\times\vec b=2\hat i-\hat k and a⃗⋅b⃗=3\vec a\cdot\vec b=3. Then the projection of b⃗\vec b on the vector a⃗−b⃗\vec a-\vec b is :

Choose one option
Answer and worked solution

Official answer: A

Recover b. a⃗×(a⃗×b⃗)=(a⃗⋅b⃗)a⃗−∣a⃗∣2b⃗\vec a\times(\vec a\times\vec b)=(\vec a\cdot\vec b)\vec a-|\vec a|^2\vec b gives b⃗=16(3a⃗−a⃗×c⃗)=(13,−43,23)\vec b=\frac16\left(3\vec a-\vec a\times\vec c\right)=\left(\frac13,-\frac43,\frac23\right) with c⃗=2i^−k^\vec c=2\hat i-\hat k.

Projection. a⃗−b⃗=(23,13,43)\vec a-\vec b=\left(\frac23,\frac13,\frac43\right); 2/321/3=221\dfrac{2/3}{\sqrt{21}/3}=\dfrac2{\sqrt{21}}.

(A)

Topics:Cross productScalar and vector triple products
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