If V-1-2-3k- and V-2-a-b-ck- where a- b- c -1- 0- 1- 2- 3 then find the numbers of non-zero vectors V-2 which are normal to V-1-

∵ V⃗ ⃗_⃗ ⃗2⃗ is normal to V⃗ ⃗_⃗ ⃗1⃗ ⇒ V⃗ ⃗_⃗ ⃗1⃗ .V⃗ ⃗_⃗ ⃗2⃗ =0 ⇒ ( i⃗ 2j⃗ +k⃗ #160; ) ( ai⃗ +bj⃗ +ck⃗ #160; ) =0 ⇒ a 2b+3c ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Definition of Vector

If V⃗1=î-2ĵ...

Question

If ${\to V}_{1} =^i - 2^j + 3^k$ and ${\to V}_{2} = a^i + b^j + c^k$ where $a, b, c \in {- 1, 0, 1, 2, 3}$ then find the numbers of non-zero vectors ${\to V}_{2}$ which are normal to ${\to V}_{1}$ .

Open in App

Solution

Suggest Corrections

Similar questions

{\to v}_{1}, {\to v}_{2}

{\to v}_{3}

{\to v}_{1} = {\to v}_{2} - {\to v}_{3}

{\to v}_{1} = (\to a \times ˆ i) \times ˆ i

{\to v}_{2} = (\to a \times ˆ j) \times ˆ j

{\to v}_{3} = (\to a \times ˆ k) \times ˆ k

\to a

¯ a, ¯ b, ¯ c

_{1},_{2},_{3}

_{1} = \frac{\to b \times \to c}{[\to a \to b \to c]},_{2} = \frac{\to c \times \to a}{[\to a \to b \to c]},_{3} = \frac{\to a \times \to b}{[\to a \to b \to c]}

{\to V}_{1} =^i + 2^j + 2^k

{\to V}_{2} = 2^i + 3^j - 4^k

\to p =^i +^j +^k

\to q = a^i + b^j + c^k

a, b, c \to {- 2, - 1, 0, 1, 2}

\to q

\to a

\to 1

{\to v}_{1}

{\to v}_{2}

Join BYJU'S Learning Program