JEE Advanced · MathematicsEasy

$If the vectors u = 2 \hat{i} - \hat{j} + \hat{k} and v = \hat{i} + 2 \hat{j} - 3 \hat{k} are given, find their dot product u \cdot v .$

A. $0$
B. $3$
C. $- 3$
D. $1$

Show correct answer & step-by-step solution

Correct answer: C — $- 3$

Solution

$The dot product u \cdot v is calculated as (u_{x} v_{x}) + (u_{y} v_{y}) + (u_{z} v_{z}) .$
$Substitute the components: (2) (1) + (- 1) (2) + (1) (- 3) .$
$Calculate the sum: $2 - 2 - 3 = -3$.$
$Hence the answer is (C).$

Attempt this question & track your score

Sign up free to answer, get instant scoring, and let SolveGini track which Mathematics topics you need to revise.

Attempt & Track Free →

More Vector Algebra practice questions

View all Vector Algebra questions →