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Properties of Determinants

If X and Y co...

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If X and Y components of a vector \overrightarrow Phave numerical value 2 and 3 respectively and that of \overrightarrow{P } + \overrightarrow Qhave magnitudes 6 and 8. Find the magnitude of \overrightarrow Q

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Q. Suppose that

\to p, \to q

\to r

are three non-coplanar vectors in

R^{3} .

Let the components of a vector

\to s

\to p, \to q,

\to r

4, 3,

5,

respectively. If the components of this vector

\to s

(- \to p + \to q + \to r),

(\to p - \to q + \to r),

(- \to p - \to q + \to r),

x, y,

z,

respectively, then the value of

2 x + y + z

Q. Suppose that

\to p, \to q

\to r

are three non-coplanar vectors in

R^{3} .

Let the components of a vector

\to s

\to p, \to q,

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4, 3,

5,

respectively. If the components of this vector

\to s

(- \to p + \to q + \to r),

(\to p - \to q + \to r),

(- \to p - \to q + \to r),

x, y,

z,

respectively, then the value of

2 x + y + z

Q. Find the angle between two vectors

\to a

\to b

with magnitudes

\sqrt{3}

2

respectively such that

\to a . \to b = \sqrt{6}

.

Q. The magnitude of components of a vector

\to a

along x and y axis respectively are

Vectors $\to C$ and $\to D$ have magnitudes of 3 and 4 units respectively. What is the angle between the directions of $\to C$ and $\to D$ if the magnitude of vector product $\to C \times \to D$ is x and y respectively?

(x) 0 (y) 12 units

(i) 0 (ii) $\frac{π}{2}$ (iii) $\frac{π}{3}$ (iv) $\frac{π}{4}$

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