Question Question 3 Determine whether the line (1+t, 2 - t, 4t) is parallel, orthogonal, or neither to the given plane. 1. (enter a, b, or c) a (1 + t, 2-t, 4t) is parallel to the plane x - y + 4z = 5. b (1+t, 2 - t, 4t) is orthogonal to the plane x - y + 4z = 5. c neither 2. (enter (a, b, or c) a (1+t, 2 - t, 4t) is parallel to the plane 2x – 2y - 2=1. b (1 + t, 2 - t, 4t) is orthogonal to the plane 2x – 2y - 2=1. C neither

IJXHL2 The Asker · Calculus

Transcribed Image Text: Question 3 Determine whether the line (1+t, 2 - t, 4t) is parallel, orthogonal, or neither to the given plane. 1. (enter a, b, or c) a (1 + t, 2-t, 4t) is parallel to the plane x - y + 4z = 5. b (1+t, 2 - t, 4t) is orthogonal to the plane x - y + 4z = 5. c neither 2. (enter (a, b, or c) a (1+t, 2 - t, 4t) is parallel to the plane 2x – 2y - 2=1. b (1 + t, 2 - t, 4t) is orthogonal to the plane 2x – 2y - 2=1. C neither

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we know thotfor orthogund line and pleine\vec{d}=k \vec{n}for parallel line and plane\vec{d} \cdot \vec{n}=0given 11 n t is (1+t, 2-t, 4 t)d^{\prime}=(1,-1,4)(1)\begin{array}{r}x-y+4 z=5 \\\vec{n}=(1,-1,4) \\\text { clearly } \vec{d}=\vec{n}\end{array}\therefore orthugonalcorrect option (b)(1+t, 2-d, 4 t) is ortho gond to the planex-y+4 z=5(2)\begin{array}{l} 2 x-2 y-2=1 \\\vec{n}=(2,-2,-1) \\\vec{d} \cdot \vec{n}=1 \times 2+2 \times 1-9 \times 1 \\=2+2-4 \\=0 \\\vec{d} \cdot \vec{n}=0 \quad \text { (paralle1) }\end{array}correct optien a)[+t, 2-t, A t) is paralel w the plane.2 x-2 y \neq z=1 ...