If a=i^+2j^+3k^,b=i^+λj^+4k^,c=2i^+4j^+(λ2−1)k^ then find the non zero value of a×c, given a,b and c are coplanar (A) 2i^−j^ (B) −10i^+5j^ (C) 2i^+j^ (D) i^+j^+j^k

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If {{a}}={{i}}+{2}{{j}}+{3}{{k}},{{b}}={{i}}+{{j}}+{4}{{k}},{{

Question

If $a = \hat{i} + 2 \hat{j} + 3 \hat{k}, b = \hat{i} + λ \hat{j} + 4 \hat{k}, c = 2 \hat{i} + 4 \hat{j} + (λ^{2} - 1) \hat{k}$ then find the non zero value of $a \times c$ , given $a, b$ and $c$ are coplanar (A) $2 \hat{i} - \hat{j}$ (B) $- 10 \hat{i} + 5 \hat{j}$ (C) $2 \hat{i} + \hat{j}$ (D) $\hat{i} + \hat{j} + \hat{j} k$

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a = \hat{i} + 2 \hat{j} + 3 \hat{k}, b = \hat{i} + λ \hat{j} + 4 \hat{k}, c = 2 \hat{i} + 4 \hat{j} + (λ^{2} - 1) \hat{k}

then find the non zero value of

a \times c

, given

a, b

and

c

are coplanar (A)

2 \hat{i} - \hat{j}

(B)

- 10 \hat{i} + 5 \hat{j}

(C)

2 \hat{i} + \hat{j}

(D)

\hat{i} + \hat{j} + \hat{j} k

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Question Text

a = \hat{i} + 2 \hat{j} + 3 \hat{k}, b = \hat{i} + λ \hat{j} + 4 \hat{k}, c = 2 \hat{i} + 4 \hat{j} + (λ^{2} - 1) \hat{k}

then find the non zero value of

a \times c

, given

a, b

and

c

are coplanar (A)

2 \hat{i} - \hat{j}

(B)

- 10 \hat{i} + 5 \hat{j}

(C)

2 \hat{i} + \hat{j}

(D)

\hat{i} + \hat{j} + \hat{j} k