If the vectors 3i + j - k and 2i - j + mk are perpendicular, then the value of m is

D. 5 — Two vectors are perpendicular if their dot product is zero. Calculating the dot product gives (3)(2) + (1)(-1) + (-1)(m) = 0, which simplifies to 6 - 1 - m = 0, so m = 5.

JEE Main · MathematicsMedium

$If the vectors 3 \hat{i} + \hat{j} - \hat{k} and 2 \hat{i} - \hat{j} + m \hat{k} are perpendicular, then the value of m is$

A. $2$
B. $3$
C. $4$
D. $5$

Show correct answer & step-by-step solution

Correct answer: D — $5$

Solution

Two vectors are perpendicular if their dot product is zero. Thus, (3) (2) + (1) (- 1) + (- 1) (m) = 0, which implies $6 - 1 - m = 0$, so m = 5 .

Attempt this question & track your score

Attempt & Track Free →

More Vector Algebra practice questions

$Find the magnitude of the vector a = 3i + 4j - 12k.$
$If the magnitude of a vector a is 5, what is the magnitude of 3a?$
$If the vectors 2i + aj + k and 3i - 2j + 4k are perpendicular, find the value of a.$
$What is the projection of vector i + j on vector i - j?$
$Let a and b be two unit vectors such that the angle between them is 60 degrees. Then the value of |a - b| is$
$If a = 2i + 2j + k and b = 6i - 3j + 2k, then the projection of a on b is$
$The area of a triangle whose adjacent sides are represented by the vectors a = 3i + j + 2k and b = i - j + k is$
$If the vectors a = i + j + k, b = i - j + 2k, and c = x i + (x - 2) j - k are coplanar, then find the value of x.$
$Let a and b be two vectors such that |a| = 1, |b| = 4, and a dot b = 2. If c = (2a x b) - 3b, then find the angle betwee$
$Let a, b, and c be three unit vectors such that a + b + c = 0. If the vector d = a x b + b x c + c x a, then what is the$

View all Vector Algebra questions →

If the vectors 3i^+j^​−k^ and 2i^−j^​+mk^ are perpendicular, then the value of m is

Solution

Attempt this question & track your score

More Vector Algebra practice questions

$If the vectors 3 \hat{i} + \hat{j} - \hat{k} and 2 \hat{i} - \hat{j} + m \hat{k} are perpendicular, then the value of m is$