Three 3 dim vectors, one with a parameter $\lambda$ in the third coordinate. Find value of $\lambda$ ensuring vectors coplanar. Scalar triple product.

Gradient of $f(x,y,z)$.

Should include a warning to insert * between multiplied terms

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Gradient of $f(x,y,z)$.

Should warn that multiplied terms need * to denote multiplication.

Find all points for which the gradient of a scalar field is orthogonal to the $z$-axis.

Should warn that multiplied terms need * to denote multiplication.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

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Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

5 questions on vectors. Scalar product, angle between vectors, cross product, when are vectors perpendicular, combinations of vectors defined or not.

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Some basic tasks involving vectors, including converting to/from component form, scalar product, resultant vectors.

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant

Add three vectors by determining their scalar components, summing them and then resolving the rectangular components to find the magnitude and direction of the resultant.

Add three vectors by determining their scalar components and summing them.

Directional derivative of a scalar field.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Addition, subtraction and multiplication of 2 x 2 matrices and multiplication by a scalar.

(Last three parts of original question removed.)

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Addition, subtraction and multiplication of 2 x 2 matrices and multiplication by a scalar.

(Last three parts of original question removed.)

Quiz to assess matrix addition, subtraction, multiplication and multiplication by scalar, determinants and inverses, solving a system of simultaneous equations.

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Elementary operations on vectors; sum, modulus, unit vector, scalar multiple. 

Addition, subtraction and multiplication of 2 x 2 matrices and multiplication by a scalar.

(Last three parts of original question removed.)