Cross Product

Cyclic Rule: For Right-Handed Coordinate Systems:
- $\hat{i} \times \hat{j} = \hat{k}$
- $\hat{j} \times \hat{k} = \hat{i}$
- $\hat{k} \times \hat{i} = \hat{j}$
Anti-cyclical: Reversing the order flips the sign (e.g., $\hat{j} \times \hat{i} = - \hat{k}$ ).
Geometry: The unit vector $\hat{k}$ is perpendicular to the $x y$ -plane containing $\hat{i}$ and $\hat{j}$ .

This easy difficulty mathematics question is from the chapter vector algebra, covering the topic of cross product. It appeared in the 2025 exam.

Looking for more practice? Explore all mathematics questions or browse vector algebra questions on RankGuru.

Cross Product

Select the correct option:

🔒 Solution Hidden from View

More vector algebra Practice Questions

For the vectors a = i + j + k and b = 2i - j + 3k, determine the magnitude of their vector product a...

The magnitude of cross product of two vectors a and b is

If two vectors are parallel, their cross product is

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 -...

About This Question

Solution

The magnitude of cross product of two vectors $a$ and $b$ is