Two vectors Vector a = a1i +a2j +a3k and Vector B = b1i+b2j+b3k are collinear if (a) a1b1 + a2b2 + a3b3 = 0

Question

Two vectors \(\vec{a} = a_1\hat{i}+ a_2\hat{j}+a_3\hat{k}\) and \(\vec{b} = b_1\hat{i} +b_2\hat{j}+b_3\hat{k}\)

are collinear if

(a) a₁b₁ + a₂b₂ + a₃b₃ = 0

(b) \(\frac{a_1 }{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}\)

(c) a₁ = b₁, a₂ = b₂, a₃ = b₃

(d) a₁ + a₂ + a₃ = b₁ + b₂ + b₃

Answer 1

Correct option is : \((b) \ \frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3}\) 

If two vectors \(\vec{a}= a_1\hat i +a_2\hat j+a_3\hat k \ \text{and} \ \vec{b}= b_1\hat{i}+b_2\hat j +b_3\hat {k}\) are collinear.

Then \( \ \frac{a_1}{b_1} = \frac{a_2}{b_2} = \frac{a_3}{b_3} = \lambda\)