If $\vec a$ and $\vec b$ are unit vectors such that $[\vec a,\vec b,\vec a\times\vec b]=\dfrac14$, then the angle between $\vec a$ and $\vec b$ is (1) $\pi/6$ (2) $\pi/4$ (3) $\pi/3$ (4) $\pi/2$

If vec a and vec b are unit vectors such that [vec a,vec b,vec a×vec b]=dfrac14, then the angle between vec a

Exercise 6.10 · Q7

\vec a

(1)

\pi/6

(2)

\pi/4

(3)

\pi/3

(4)

\pi/2

Puducherry TnboardTextbookSubjectiveImportance★★★★★

49% · 80/162 Questions

🔒 Locked · start free trial →

You're viewing a preview — the full solution, concept, methods & PYQ mapping are locked.

Start your 14-day free trial to unlock the full solution →

Setting $\vec c=\vec a\times\vec b$ in the scalar triple product $[\vec a,\vec b,\vec c]=(\vec a\times\vec b)\cdot\vec c$ makes it dot with itself, i.e. the squared magnitude of $\vec a\times\vec b$ — which is $\sin^2\theta$ for unit vectors.

Step 1. Rewrite the bracket. $[\vec a,\vec b,\vec a\times\vec b]=(\vec a\times\vec b)\cdot(\vec a\times\vec b)=|\vec a\times\vec b|^2$ . …

Start your 14-day free trial to unlock the full solution →

←Previous question · 6.11Q6 — The volume of the parallelepiped with its edges represented by the vec…→Next question · 6.11Q8 — If vec a=hat i+hat j+hat k,vec b=hat i+hat j,vec c=hat i and (vec a×ve…

Q.If $\vec a$ and $\vec b$ are unit vectors such that $[\vec a,\vec b,\vec a\times\vec b]=\dfrac14$ , then the angle between $\vec a$ and $\vec b$ is

Concept understanding — Scalar Triple Product and Coplanarity

Scalar Triple Product and Coplanarity

Q.If a⃗\vec aa and b⃗\vec bb are unit vectors such that [a⃗,b⃗,a⃗×b⃗]=14[\vec a,\vec b,\vec a\times\vec b]=\dfrac14[a,b,a×b]=41​, then the angle between a⃗\vec aa and b⃗\vec bb is

🎓Unlock everything free for 14 days

Q.If $\vec a$ and $\vec b$ are unit vectors such that $[\vec a,\vec b,\vec a\times\vec b]=\dfrac14$ , then the angle between $\vec a$ and $\vec b$ is

Unlock everything free for 14 days