Let a - i - j - k - b - i - and c - c 1 i - c 2 j - c 3 k - - Then-i If c1-1 and c2-2- find c3 which makes a - - b - and c - coplanar-ii If c2-1 and c3-1- show that no value of c1 can make a - - b - and c - coplanar-

I #160;If #160;c1=1 #160;and #160;c2=2, #160;then #160;a #8594;=i^+j^+k^, #160;b #8594;=i^ #160;and #160;c^=i^+2j^+c3k^.We #160;know # ...

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Bisector of Angle between Two Vectors

Let a →= i ∧∧...

Question

$Let \vec{a} = \hat{i} + \hat{j} + \hat{k}, \vec{b} = \hat{i} and \hat{c} = c_{1} \hat{i} + c_{2} \hat{j} + c_{3} \hat{k} . Then,$
(i) If c₁ = 1 and c₂ = 2, find c₃ which makes $\vec{a,} \vec{b} and \vec{c}$ coplanar.

(ii) If c₂ = −1 and c₃ = 1, show that no value of c₁ can make $\vec{a,} \vec{b} and \vec{c}$ coplanar.

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

\to b =^i

\to c = c_{1}^i + c_{2}^j + c_{3}^k

c_{2} = - 1

c_{3} = 1

c_{1}

(a, b)

\to c

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

\to b =^i

\to c = c_{1}^i + c_{2}^j + c_{3}^k

c_{1} = 1

c_{2} = 2

c_{3}

(a, b)

\to c

\vec{a} = a_{1} \hat{i} + a_{2} \hat{j} + a_{3} \hat{k}, \vec{b} = b_{1} \hat{i} + b_{2} \hat{j} + b_{3} \hat{k} and \vec{c} = c_{1} \hat{i} + c_{2} \hat{j} + c_{3} \hat{k},

\vec{a} \times (\vec{b} + \vec{c}) = \vec{a} \times \vec{b} + \vec{a} \times \vec{c} .

a_{1} b_{1} c_{1}, a_{2} b_{2} c_{2}

a_{3} b_{3} c_{3}

Δ = ∣ ∣ ∣ ∣ \begin{matrix} c_{1} & a_{1} & b_{1} c_{2} & a_{2} & b_{2} c_{3} & a_{3} & b_{3} \end{matrix} ∣ ∣ ∣ ∣

Δ

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