Perpendicular Vectors

Question

Find the scalar value m so that the vector 2i + m j + k becomes perpendicular to the vector i - 3j + 2k in space.

RankGuru · Accepted Answer

Two vectors are perpendicular exactly when their dot product equals zero, since cos(90 degrees) = 0 forces the scalar product to vanish. Imposing the orthogonality condition and solving for the unknown is a frequent JEE Advanced parameter problem. Compute the dot product of (2, m, 1) and (1, -3, 2): (2)(1) + (m)(-3) + (1)(2) = 2 - 3m + 2 = 4 - 3m. Setting this equal to zero gives 4 - 3m = 0, so 3m = 4 and m = 4/3. Option 3/4 inverts the fraction by dividing incorrectly. Option -4/3 drops a sign when isolating m. Option 2 ignores the j-contribution entirely, solving only the constant terms. The positive value 4/3 is the unique scalar making the angle exactly 90 degrees. Geometrically, adjusting m tilts the first vector until its projection onto the second cancels to zero. Plausibility check: substituting m = 4/3 back gives 4 - 3(4/3) = 4 - 4 = 0, confirming the dot product vanishes and the vectors are indeed orthogonal.

Perpendicular Vectors

Select the correct option:

🔒 Solution Hidden from View

More vector algebra Practice Questions

Two vectors of magnitudes 5 and 12 act at a point with an included angle of 90 degrees; evaluate the...

If the scalar triple product [a b c] equals 7 for three given vectors, what is the value of the rear...

For two vectors with magnitudes 4 and 3 enclosing a 30 degree angle, evaluate the sum of squares |a ...

Three unit vectors a, b and c satisfy a + b + c = 0; using this constraint, evaluate the sum a . b +...

The shortest distance between two skew lines is computed using which expression involving their dire...

Determine the value of the scalar t for which the vectors i + 2j, 2i + tj and the resulting set beco...

A point P divides the line segment joining A(1,2,3) and B(4,8,9) internally in the ratio 2:1; locate...

If two nonzero vectors a and b satisfy |a + b| = |a - b|, what can be concluded about the angle betw...

What is the unit vector directed along the vector obtained by adding a = 2i - j + 2k and b = i + j -...

A vector makes equal acute angles with all three coordinate axes; determine the value of each of its...

Three coterminous edges of a parallelepiped are a = i + j, b = j + k and c = k + i; calculate the vo...

For what value of the scalar lambda are the three vectors i + j + k, i + lambda j + 2k and 2i + j + ...

About This Question

Solution