If , , , then…

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

\mathbf{a} = x\hat{\mathbf{i}} + y\hat{\mathbf{j}} + z\hat{\mathbf{k}}

\mathbf{b} = y\hat{\mathbf{i}} + z\hat{\mathbf{j}} + x\hat{\mathbf{k}}

\mathbf{c} = z\hat{\mathbf{i}} + x\hat{\mathbf{j}} + y\hat{\mathbf{k}}

, then

\mathbf{a} \times (\mathbf{b} \times \mathbf{c})

is (1) parallel to

(y - z)\hat{\mathbf{i}} + (z - x)\hat{\mathbf{j}} + (x - y)\hat{\mathbf{k}}

(2) orthogonal to

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

(3) orthogonal to

(y + z)\hat{\mathbf{i}} + (z + x)\hat{\mathbf{j}} + (x + y)\hat{\mathbf{k}}

(4) parallel to

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