Vector Algebra
Coplanar Vectors
Grade 12
Question:
<p><strong>Ex. 99</strong> Which of the following is true?</p>
<p>(a) <strong>a</strong> and <strong>a</strong>₂ are collinear</p>
<p>(b) <strong>a</strong>₁ and <strong>c</strong> are collinear</p>
<p>(c) <strong>a</strong>, <strong>a</strong>₁ and <strong>b</strong> are coplanar</p>
<p>(d) <strong>a</strong>, <strong>a</strong>₁ and <strong>a</strong>₂ are coplanar</p>
Step-by-Step Solution
Key Concept: A projection of a vector lies in the direction of the vector it is projected onto. The original vector, its projection, and the direction vector are always coplanar.
Step 1: a _1 is the projection of a on b , so a _1 is in the direction of b . Step 2: Since a _1 is parallel (collinear) to b , the vectors a , a _1, and b all lie in the same plane. Step 3: Therefore, a , a _1, and b are coplanar. ∴ Answer is (c).
Correct Answer: C