Question

If (2i + 3j + xk) and (14i + 21j + 7k) are parallel, the value of x is​

Answer 1

Explanation:

parallel vectors have proportional direction ratios

Therefore 14/2=21/3=7/x

Solving for x we get x=1

Answer 2

Correct Question :

Vector A = 2i + 3j + xk and Vector B 14i + 21j +7k. If A and B Vector are parallel, then find the value of x.

AnsWer :

1.

Solution :

• When two vector parallel to then, a1/a2 = b1 /b2 = c1/c2.

Let the,

$\tt \vec{A} = 2 \hat{i} + 3 \hat{j} + x \hat{k}. \\ \tt \vec{B} = 14 \hat{i} + 21 \hat{j} + 7 \hat{k}.$

$\tt \frac{ a_1}{a_2} = \frac{b_1 }{b _2 } = \frac{c _ 1}{c_2}$

$\tt \implies\frac{2}{14} = \frac{3}{21} = \frac{x}{7}$

$\tt \implies \frac{ \cancel2}{ \cancel{14}} = \frac{ \cancel3}{ \cancel{21}} = \frac{x}{7}$

$\implies \tt \frac{1}{7} = \frac{1}{7} = \frac{x}{7}$

$\implies \tt \frac{1}{7} = \frac{x}{7}$

$\implies \tt x = \frac{\cancel7}{\cancel7}$

$\tt \implies x = 1.$

Therefore,the value of x be 1.