<!-- NEW5 — TEST 5 · THE BEND AT THE HEART · part 35 -->
ector with the same direction as this one, but
	 * with the specified length.
	 *
	 * @param {number} length - The new length of this vector.
	 * @return {Vector3} A reference to this vector.
	 */
	setLength( length ) {

		return this.normalize().multiplyScalar( length );

	}

	/**
	 * Linearly interpolates between the given vector and this instance, where
	 * alpha is the percent distance along the line - alpha = 0 will be this
	 * vector, and alpha = 1 will be the given one.
	 *
	 * @param {Vector3} v - The vector to interpolate towards.
	 * @param {number} alpha - The interpolation factor, typically in the closed interval `[0, 1]`.
	 * @return {Vector3} A reference to this vector.
	 */
	lerp( v, alpha ) {

		this.x += ( v.x - this.x ) * alpha;
		this.y += ( v.y - this.y ) * alpha;
		this.z += ( v.z - this.z ) * alpha;

		return this;

	}

	/**
	 * Linearly interpolates between the given vectors, where alpha is the percent
	 * distance along the line - alpha = 0 will be first vector, and alpha = 1 will
	 * be the second one. The result is stored in this instance.
	 *
	 * @param {Vector3} v1 - The first vector.
	 * @param {Vector3} v2 - The second vector.
	 * @param {number} alpha - The interpolation factor, typically in the closed interval `[0, 1]`.
	 * @return {Vector3} A reference to this vector.
	 */
	lerpVectors( v1, v2, alpha ) {

		this.x = v1.x + ( v2.x - v1.x ) * alpha;
		this.y = v1.y + ( v2.y - v1.y ) * alpha;
		this.z = v1.z + ( v2.z - v1.z ) * alpha;

		return this;

	}

	/**
	 * Calculates the cross product of the given vector with this instance.
	 *
	 * @param {Vector3} v - The vector to compute the cross product with.
	 * @return {Vector3} The result of the cross product.
	 */
	cross( v ) {

		return this.crossVectors( this, v );

	}

	/**
	 * Calculates the cross product of the given vectors and stores the result
	 * in this instance.
	 *
	 * @param {Vector3} a - The first vector.
	 * @param {Vector3} b - The second vector.
	 * @return {Vector3} A reference to this vector.
	 */
	crossVectors( a, b ) {

		const ax = a.x, ay = a.y, az = a.z;
		const bx = b.x, by = b.y, bz = b.z;

		this.x = ay * bz - az * by;
		this.y = az * bx - ax * bz;
		this.z = ax * by - ay * bx;

		return this;

	}

	/**
	 * Projects this vector onto the given one.
	 *
	 * @param {Vector3} v - The vector to project to.
	 * @return {Vector3} A reference to this vector.
	 */
	projectOnVector( v ) {

		const denominator = v.lengthSq();

		if ( denominator === 0 ) return this.set( 0, 0, 0 );

		const scalar = v.dot( this ) / denominator;

		return this.copy( v ).multiplyScalar( scalar );

	}

	/**
	 * Projects this vector onto a plane by subtracting this
	 * vector projected onto the plane's normal from this vector.
	 *
	 * @param {Vector3} planeNormal - The plane normal.
	 * @return {Vector3} A reference to this vector.
	 */
	projectOnPlane( planeNormal ) {

		_vector$c.copy( this ).projectOnVector( planeNormal );

		return this.sub( _vector$c );

	}

	/**
	 * Reflects this vector off a plane orthogonal to the given normal vector.
	 *
	 * @param {Vector3} normal - The (normalized) normal vector.
	 * @return {Vector3} A reference to this vector.
	 */
	reflect( normal ) {

		return this.sub( _vector$c.copy( normal ).multiplyScalar( 2 * this.dot( normal ) ) );

	}
	/**
	 * Returns the angle between the given vector and this instance in radians.
	 *
	 * @param {Vector3} v - The vector to compute the angle with.
	 * @return {number} The angle in radians.
	 */
	angleTo( v ) {

		const denominator = Math.sqrt( this.lengthSq() * v.lengthSq() );

		if ( denominator === 0 ) return Math.PI / 2;

		const theta = this.dot( v ) / denominator;

		// clamp, to handle numerical problems

		return Math.acos( clamp( theta, -1, 1 ) );

	}

	/**
	 * Computes the distance from the given vector to this instance.
	 *
	 * @param {Vector3} v - The vector to compute the distance to.
	 * @return {number} The distance.
	 */
	distanceTo( v ) {

		return Math.sqrt( this.distanceToSquared( v ) );

	}

	/**
	 * Computes the squared distance from the given vector to this instance.
	 * If you are just comparing the distance with another distance, you should compare
	 * the distance squared instead as it is slightly more efficient to calculate.
	 *
	 * @param {Vector3} v - The vector to compute the squared distance to.
	 * @return {number} The squared distance.
	 */
	distanceToSquared( v ) {

		const dx = this.x - v.x, dy = this.y - v.y, dz = this.z - v.z;

		return dx * dx + dy * dy + dz * dz;

	}

	/**
	 * Computes the Manhattan distance from the given vector to this instance.
	 *
	 * @param {Vector3} v - The vector to compute the Manhattan distance to.
	 * @return {number} The Manhattan distance.
	 */
	manhattanDistanceTo( v ) {

		return Math.abs( this.x - v.x ) + Math.abs( this.y - v.y ) + Math.abs( this.z - v.z );

	}

	/**
	 * Sets the vector components from the given spherical coordinates.