If a = i + j +2 k and b =2 i + j -2 k , find the unit vector in the direction of: 1. 6 b 2. 2 a - b

Here, a = i + j +2 k and b =2 i + j -2 k 1. 6 b =12 i +6 j -12 k Unit vectors in the direction of 6 b = 6 b |6 b | = 12 i +6 j -12 k 12^2+6^2+12^2 = 6(12 i + j -2 k ) 324 = 6(2 i + j -2 k ) 18 = 2 i + j -2 k 3 2. 2 a - b =2( i + j +2 k ) = j +6 k Unit vectors in the direction of 2 a - b = 2 a - b |2 a - b | = j +6 k 1^2+6^2 = j +6 k 37

If a = i + j +2 k and b =2 i + j -2 k , find the unit vector in t…

Download App

Question

If $\vec{\text{a}}=\vec{\text{i}}+\vec{\text{j}}+2\vec{\text{k}}$ and $\vec{\text{b}}=2\vec{\text{i}}+\vec{\text{j}}-2\vec{\text{k}},$ find the unit vector in the direction of:

$6\vec{\text{b}}$
$2\vec{\text{a}}-\vec{\text{b}}$

✓

Answer

Here, $\vec{\text{a}}=\vec{\text{i}}+\vec{\text{j}}+2\vec{\text{k}}$ and $\vec{\text{b}}=2\vec{\text{i}}+\vec{\text{j}}-2\vec{\text{k}}$

$6\vec{\text{b}}=12\hat{\text{i}}+6\hat{\text{j}}-12\hat{\text{k}}$

$\therefore$ Unit vectors in the direction of $6\vec{\text{b}}=\frac{6\vec{\text{b}}}{|6\vec{\text{b}}|}$

$=\frac{12\hat{\text{i}}+6\hat{\text{j}}-12\hat{\text{k}}}{\sqrt{12^2+6^2+12^2}}$

$=\frac{6(12\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}})}{\sqrt{324}}$

$=\frac{6(2\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}})}{18}$

$=\frac{2\hat{\text{i}}+\hat{\text{j}}-2\hat{\text{k}}}{3}$

$2\vec{\text{a}}-\vec{\text{b}}=2(\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}})$

$=\hat{\text{j}}+6\hat{\text{k}}$

$\therefore$ Unit vectors in the direction of $2\vec{\text{a}}-\vec{\text{b}}$

$=\frac{2\vec{\text{a}}-\vec{\text{b}}}{|2\vec{\text{a}}-\vec{\text{b}}|}=\frac{\hat{\text{j}}+6\hat{\text{k}}}{\sqrt{1^2+6^2}}$

$=\frac{\hat{\text{j}}+6\hat{\text{k}}}{\sqrt{37}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from DIFFERENTIAL EQUATIONS→DIFFERENTIAL EQUATIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Answer

Need a full question paper?

Explore more

Similar questions